Document:

<PAGE>   1
                                                                   EXHIBIT 10.10

                        AMENDMENT TO EMPLOYMENT AGREEMENT

         This Amendment to Employment Agreement ("Amendment"), entered into as
of June 1, 2000, by and between AMEDISYS, INC., a Delaware corporation (the
"Company"), and LARRY GRAHAM ("GRAHAM").

         WHEREAS, Company and GRAHAM are parties to that certain Employment
Agreement dated February 1, 2000 (the "Agreement"), whereby the Company and
GRAHAM agreed, among other things, on the terms and condition of GRAHAM's
employment and severance with the Company.

         WHEREAS, the Company and GRAHAM desire to amend the Agreement as
specifically set forth herein.

         NOW, THEREFORE, the parties mutually agree as follows:

         1. RECITATIONS. The above recitations are incorporated herein by this
reference.

         2. MODIFICATIONS TO THE AGREEMENT. The following provision shall be
inserted into the Agreement as Section 3.4(b), to be included in the Agreement's
definition of "Change of Control":

"(b) The individuals who serve on the Company's Board of Directors as of the
effective date of this Agreement (the "Incumbent Board") cease for any reason to
constitute at least a majority of the Board of Directors of the Company;
provided, however, any person who becomes a director subsequent to the effective
date of this Agreement, whose election or nomination for election by the
Company's shareholders was approved by a vote of at least a majority of the
directors then compiling the Incumbent Board, shall for purposes of this
Agreement be considered as if such person was a member of the Incumbent Board."

         3. EFFECT OF THIS AMENDMENT. Except as specifically stated herein, the
execution and delivery of this Amendment shall in no way affect the respective
obligations of the parties under the Agreement, all of which shall continue in
full force and effect.

         4. SUCCESSORS AND ASSIGNS. This Amendment shall be binding upon and
inure to the benefit of the parties hereto and their respective successors and
assigns.

         IN WITNESS WHEREOF, the parties hereto have cause this Amendment to be
executed, effective as of the date and year first written above.

                                             AMEDISYS, INC.

                                             By: /s/ WILLIAM F. BORNE
                                                --------------------------------
                                                      William F. Borne, CEO

                                                 /s/ LARRY GRAHAM
                                             -----------------------------------
                                                          LARRY GRAHAM<PAGE>   1
                                                                   EXHIBIT 10.11

                              EMPLOYMENT AGREEMENT

                                     BETWEEN

                                 AMEDISYS, INC.

                                       AND

                                  JOHN JOFFRION

                                  June 1, 2000

<PAGE>   2

                              EMPLOYMENT AGREEMENT

               THIS EMPLOYMENT AGREEMENT ("Agreement") entered into as of the
1st day of June, 2000, and continuing for an indefinite duration, by and between
AMEDISYS, INC., a Delaware corporation (the "Company") and JOHN JOFFRION
("JOFFRION").

                                    RECITALS:

               A. The Company owns, manages and/or operates agencies and
facilities for the provision of home health, alternate site infusion therapy and
ambulatory surgery health care services (the "Business").

               B. JOFFRION is employed by the Company as the Senior Vice
President of Finance;

               NOW, THEREFORE, in consideration of the mutual promises and
covenants contained in this Agreement, the parties agree as follows:

               1. RECITATIONS. The above recitations are incorporated herein by
this reference.

               2. PERFORMANCE OF DUTIES. JOFFRION shall perform such duties as
are usually performed by the Senior Vice President of Finance of health care
companies of a business similar in size and scope as the Company and such other
reasonable additional duties as may be prescribed from time to time by the
Company's Chief Executive Officer which are reasonable and consistent with the
expectations of the Company and the Company's operations, taking into account
JOFFRION's expertise and job responsibilities, including but not limited to,
adherence to internal compliance and governmental and regulatory rules,
regulations and applicable laws. JOFFRION shall report directly to the Chief
Executive Officer of the Company or his designee.

                    2.1 Devotion of Time. JOFFRION agrees to devote full time
and attention to the business and affairs of the Company to the extent necessary
to discharge the responsibilities assigned to JOFFRION and to use reasonable
best efforts to perform faithfully and efficiently such responsibilities.

               3. TERMINATION OF EMPLOYMENT.

                    3.1 Termination of Employment by the Company for Cause. The
Company may terminate JOFFRION's employment for Cause, as defined herein,
without any obligation of severance payments to JOFFRION. Cause shall be defined
as follows:

                         (a) a material default or breach by JOFFRION of any of
the provisions of this Agreement materially detrimental to the Company which is
not cured within thirty (30) days following written notice thereof;

                         (b) actions by JOFFRION constituting fraud,
embezzlement or dishonesty which result in a conviction of a criminal offense
not overturned on appeal;

                         (c) intentionally furnishing materially false,
misleading, or omissive information to the Company's Chief Executive Officer,
Board of Directors or any committee of the Board of Directors, that is
materially detrimental to the Company;

                                      -2-
<PAGE>   3

                         (d) actions constituting a breach of the
confidentiality of the Business and/or trade secrets of the Company which is
materially detrimental to the Company;

                         (e) willful failure to follow reasonable and lawful
directives of the Company's Chief Executive Officer or Board of Directors, which
are consistent with JOFFRION's job responsibilities and performance which is not
cured within thirty (30) days following written notice thereof; and

                    3.2 Termination Without Cause. The Company shall have the
right to terminate JOFFRION's employment without Cause, at any time and subject
to the sole discretion of the Company. In such event, JOFFRION will cease to
have any power of his position as of the effective date of the termination.

                    3.3 Termination by JOFFRION. JOFFRION may terminate his
employment upon thirty (30) days written notice to the Company. Such notice
shall set forth in sufficient detail for the Company to understand the nature of
the facts underlying said termination.

                    3.4 Change of Control. Upon the occurrence of a "Change of
Control," if such occurs prior to JOFFRION's receiving a notice of termination
by the Company for Cause, JOFFRION shall be entitled to the Severance described
herein. "Change of Control" is defined as the following:

                         (a) The acquisition by any person, entity or "group"
within the meaning of Section 13(d) or 14(d) of the Securities Exchange Act of
1934 (the "Exchange Act") of beneficial ownership (within the meaning of Rule
13d-3 promulgated under the Exchange Act) of fifty-one (51%) percent or more of
either the then outstanding shares of the Company's common stock or the combined
voting power of the Company's then outstanding voting securities entitled to
vote generally in the election of directors; provided however, purchase by
underwriters in a firm commitment public offering of the Company's securities or
any securities purchased for investment only by professional investors shall not
constitute a Change of Control; and

                         (b) The individuals who serve on the Company's Board of
Directors as of the effective date of this Agreement (the "Incumbent Board")
cease for any reason to constitute at least a majority of the Board of Directors
of the Company; provided, however, any person who becomes a director subsequent
to the effective date of this Agreement, whose election or nomination for
election by the Company's shareholders was approved by a vote of at least a
majority of the directors then compiling the Incumbent Board, shall for purposes
of this Agreement be considered as if such person was a member of the Incumbent
Board.

               4. COMPENSATION.

                    4.1 Salary. Company shall pay to JOFFRION a base salary at
the annual rate of $136,000 (the "Base Salary"). Notwithstanding anything herein
to the contrary, the Company shall have the sole discretion at any time and from
time to time to increase the Base Salary. Base Salary shall be payable in
installments consistent with the Company's normal payroll schedule, in effect
from time to time, subject to applicable withholding and other taxes.

                    4.2 Base Salary Increases. Commencing February 1, 2001,
JOFFRION's Base Salary shall be automatically increased on February 1 of each
year during the term hereof by the greater of

                                      -3-

<PAGE>   4

(i) six (6%) percent, or (ii) $12,000.00, whichever is greater. Notwithstanding
anything herein to the contrary, the Chief Executive Officer may grant a Base
Salary Increase in excess of the amount stipulated to within this Section 4.2.

                    4.3 Bonus. At the end of each fiscal year of employment, the
Company shall pay JOFFRION a bonus up to $60,000, payable in terms which shall
be at the Company's discretion, and only if the Company attains or exceeds the
operating income (loss) as presented in the budget approved by the Company's
Board of Directors for that fiscal year, and if certain performance based
criteria which shall, from time to time, be determined by the Company and made
known to JOFFRION. Notwithstanding anything herein to the contrary, the Chief
Executive Officer may pay a bonus in excess of the amount earned pursuant to
this Section 4.3.

                    4.4 Stock Options. Effective February 1 of each year during
the term hereof, the Company shall cause to be granted to JOFFRION, pursuant to
a stock option plan duly adopted by the Company or otherwise, options to
purchase such number of shares of the Company's common stock equal to the
greater of (i) seventy five one-hundredths (.75%) percent of the number of
shares of Company common stock issued by the Company during the preceding fiscal
year; or (ii) 12,000 shares. Notwithstanding anything herein to the contrary,
JOFFRION shall not be entitled to the grant of options during any time in which
JOFFRION is receiving severance payments from the Company, as outlined below.
Notwithstanding anything herein to the contrary, the Chief Executive Officer may
recommend that the Board of Directors of the Company grant options in excess of
the amount stipulated to in this Section 4.4.

                    4.5 Severance Compensation. Should JOFFRION be terminated
without Cause, as defined herein, or should a Change of Control, as defined
herein, occur during JOFFRION's employment with Company, JOFFRION shall be
entitled to severance compensation in an amount equal to eighteen (18) months of
JOFFRION's Base Salary at the time of such Change of Control, payable at the
discretion of the Company, but at a minimum, payable by the Company via
regularly scheduled payroll distributions until the entire severance amount due
JOFFRION is paid in full.

                    4.6 Additional Benefits.

                         (a) Vacation. JOFFRION shall be entitled to the maximum
amount of paid time off for Company employees stipulated by the Company PTO
policy during each calender year of his employment with the Company. In
addition, JOFFRION shall be entitled to paid time off for the same holidays as
other employees of the Company as established by the Company's Board of
Directors.

                         (b) Reimbursement of Expenses. JOFFRION is authorized
to incur reasonable traveling and other expenses in connection with the Business
and in performance of his duties under this Agreement. JOFFRION shall be
reimbursed by the Company for all Business expenses which are reasonably
incurred by JOFFRION. All reimbursable travel expenses shall be in accordance
with mutually agreeable and reasonable policy.

                         (c) Participation in Employee Benefit Plans. JOFFRION
shall be entitled to participate, subject to eligibility and other terms
generally established by the Company's Board of Directors, in any employee
benefit plan (including but not limited to life insurance plans, long-and
short-term disability, stock option plans, group hospitalization, health, dental
care plans, (which health insurance plans shall also cover JOFFRION's
dependents) profit sharing and pension, and other benefit plans), as may be
adopted or amended by the Company from time to time.

                                      -4-
<PAGE>   5

               5. REPRESENTATION BY JOFFRION. JOFFRION hereby represents to the
Company that he is physically and mentally capable of performing his duties
hereunder and he has no knowledge of present or past physical or mental
conditions which would cause him not to be able to perform his duties hereunder.

               6. CONFIDENTIALITY AND NON-DISCLOSURE OF INFORMATION.

                    6.1 Confidentiality. JOFFRION shall not, during his
employment with the Company or any time thereafter, divulge, furnish or make
accessible to anyone, without the Company's prior written consent, any knowledge
or information with respect to any confidential or secret aspect of the Business
which if disclosed could reasonably be expected to have a material adverse
effect on the Business ("Confidential Information").

                    6.2 Ownership of Information. JOFFRION recognizes that all
Confidential Information and copies or reproductions thereof, relating to the
Company's operations and activities made or received by JOFFRION in the course
of his employment are the exclusive property of the Company, as the case may be,
and JOFFRION holds and uses same as trustee for the Company and subject to the
Company's sole control and will deliver same to the Company at the termination
of his employment, or earlier if so requested by the Company in writing. All of
such Confidential Information, which if lost or used by JOFFRION outside the
scope of his employment, could cause irreparable and continuing injury to the
Company's Business for which there may not be an adequate remedy at law.
JOFFRION acknowledges that compliance with the provisions of this Section 6 is
necessary to protect the goodwill and other proprietary interests of the Company
and is a material condition of employment.

               7. RESTRICTIVE COVENANT. As an inducement to cause the Company to
enter into this Agreement, and in consideration of the Severance obligation of
Company herein, JOFFRION covenants and agrees that during his employment and,
for a period of eighteen (18) months after he ceases to be employed by Company,
regardless of the manner or cause of termination:

                    7.1 Solicitation of Business. He will not initiate any
contact with, call upon, solicit Business from, sell or render services to any
client or patient of the Company or any Company affiliate, within any area which
the Company conducts business, a list of which is included in Schedule 7.1,
which is attached hereto and incorporated herein ("Restricted Area"), for or on
behalf of himself or any business, firm, proprietorship, corporation,
partnership, association, entity or venture primarily engaged in the business of
providing home health, alternate site infusion therapy or ambulatory surgery
services, which is a similar business as the Business ("Competing Business"),
and JOFFRION shall not directly or indirectly aid or assist any other person,
firm or corporation to do any of the aforesaid acts.

                    7.2 Solicitation of Employees. He will not directly or
indirectly, as principal, agent, owner, partner, stockholder, officer, director,
employee, independent contractor or consultant of any competing Business, or in
any individual or representative capacity hire, solicit, directly or indirectly
cause others to hire, or solicit the employment of, any officer, sales person,
agent, or other employee of the Company or any Company affiliate, for the
purpose of causing said officer, sales person, agent or other person to
terminate employment with the Company or any Company affiliate and be employed
by such competing Business.

                    7.3 Employment. He will not accept or engage employment
with, or consult, contract or otherwise provide services to, any Competing
Business operating within the Restricted Area.

                    7.4 Material Violation. A proven material violation of this
Section 7 shall constitute a material and substantial breach of this Agreement
and shall result in the imposition of the Company's

                                      -5-
<PAGE>   6

remedies contained in Section 8 herein. JOFFRION acknowledges and agrees that
proof of such personal solicitation by JOFFRION of an employee shall constitute
absolute and conclusive evidence that JOFFRION has substantially and materially
breached the provisions of this Agreement.

                    7.5 Other Employment. It is understood by and between the
parties that the foregoing covenants set forth in Sections 6 and 7 are essential
elements of this Agreement, and that but for the Agreement of JOFFRION to comply
with such covenants, the Company would not have entered into this Agreement.
Such covenants by JOFFRION shall be construed as agreements independent of any
other provision of this Agreement and the existence of any claim or cause of
action JOFFRION may have against the Company whether predicated on this
Agreement or otherwise, shall not constitute a defense to the enforcement by
Company of these covenants.

                    7.6 Defaults and Deferred Compensation.

                         (a) JOFFRION Breach. If JOFFRION breaches any
requirement of Section 7 herein, in addition to any other remedy to which the
Company may be entitled, JOFFRION shall return to the Company any Severance
already paid to JOFFRION at the time of said breach, and all of JOFFRION's
rights to receive any portion of his Severance not already paid to him shall
terminate. The right to receive unpaid Severance will not be reinstated
notwithstanding any cessation by JOFFRION of his breach of Section 7.

                    7.7 Discontinued Operations. Notwithstanding anything in
this Section 7 to the contrary, this Section 7 shall not apply to any of the
Company's product or service divisions which at the time of JOFFRION's
employment termination was considered by the Company to be a discontinued
operation.

               8. REMEDIES. JOFFRION hereby acknowledges, covenants and agrees
that in the event of a material default or breach under this Agreement, in
addition to any other remedy set forth herein:

                    8.1 Company may suffer irreparable and continuing damages as
a result of such breach and its remedy at law will be inadequate. JOFFRION
agrees that in the event of a violation or breach of this Agreement, in addition
to any other remedies available to it, Company shall be entitled to an
injunction restraining any such default or any other appropriate decree of
specific performance, with the requirement to prove actual damages or to post
any bond or any other security and to any other equitable relief the court deems
proper; and

                    8.2 Any and all of Company's remedies described in this
Agreement shall not be exclusive and shall be in addition to any other remedies
which Company may have at law or in equity including, but not limited to, the
right to monetary damages.

               9. SEVERABILITY. The invalidity of any one or more of the words,
phrases, sentences, clauses, sections, subdivisions, or subparagraphs contained
in this Agreement shall not affect the enforceability of the remaining portions
of this Agreement or any part thereof, all of which are inserted conditionally
on their being legally valid.

               10. SUCCESSORS AND ASSIGNS.

                    10.1 Successors. This Agreement shall be binding upon the
parties hereto and their successors and assigns. For purposes of this Agreement,
the term "successor" of Company shall include any person or entity, whether
direct or indirect, whether by purchase, merger, consolidation, operation of
law, assignment, or otherwise acquires or controls: (i) all or substantially all
of the assets of Company (ii) fifty-one

                                      -6-
<PAGE>   7

percent (51%) or more of the total voting capital stock, and was not affiliated
with or in common control of Company as of the date of this Agreement; or (iii)
any other Business combination with or without the consent of Company's
shareholders.

                    10.2 Assignment. This Agreement shall be non-assignable by
either Company or JOFFRION without the written consent of the other party, it
being understood that the obligations and performance of this Agreement are
personal in nature.

               11. MISCELLANEOUS.

                    11.1 Amendment. No amendment, waiver or modification of this
Agreement or any provisions of this Agreement shall be valid unless in writing
and duly executed by both parties.

                    11.2 Binding Agreement. This Agreement shall be binding upon
and inure to the benefit of the parties and their respective heirs, legal
representatives, successors and assigns.

                    11.3 Waiver. Any waiver by any party of any breach of any
provision of this Agreement shall not be considered as or constitute a
continuing waiver or waiver of any other breach of any provision of this
Agreement.

                    11.4 Captions. Captions contained in this Agreement are
inserted only as a matter of convenience or for reference and in no way define,
limit, extend, or describe the scope of this Agreement or the intent of any
provisions of this Agreement.

                    11.5 Attorneys' Fees. In the event of any litigation arising
out of this Agreement the prevailing party shall be entitled to recover from the
other party its attorneys' fees and costs, including attorneys' fees and costs
incurred on appeal.

                    11.6 Prior Agreements. This Agreement supersedes and
replaces all prior agreements between the parties hereto dealing with the
subject matter hereof.

                    11.7 Governing Law. This Agreement shall be governed by the
laws of Louisiana.

               IN WITNESS WHEREOF, the parties have executed this Agreement as
of the day and year first above written.

                                             AMEDISYS, INC.

                                             By:
                                                --------------------------------
                                                      WILLIAM F. BORNE, CEO

                                             -----------------------------------
                                                          JOHN JOFFRION

                                      -7-

<PAGE>   8
                                  SCHEDULE 7.1

<TABLE>
<CAPTION>

ALABAMA                                                            NORTH CAROLINA
COUNTIES       GEORGIA COUNTIES    TENNESSEE COUNTIES              COUNTIES            OKLAHOMA COUNTIES
-------        ----------------    ------------------              --------------      -----------------
<S>            <C>                 <C>              <C>            <C>                 <C>
Lowndes        Bibb                Anderson         Humphrey       Johnston            Creek
Perry          Crawford            Bledsoe          Clay           Franklin            Lincoln
Monroe         Jones               Blount           Jackson        Caswell             Okmulgee
Wilcox         Monroe              Bradley          Overton        Alamance            Pawnee
Chilton        Butts               Cumberland       Pickett        Chatam              Payne
Autauga        Jasper              Fentress         Putnam         Durham              Tulsa
Choctaw        Walton              Grundy           White          Orange              Washington
Clarke         Newton              Hamilton                        Person              Kay
Hale           Bartow              Loudon                          Wake                Noble
Marengo        Carroll             Marion                          Harnett             Ofuskee
Sumter         Cherokee            Meigs                           Randolph            Hughes
Madison        Clayton             Monroe                          Nash                Osage
Marshall       Cobb                Morgan                                              Rogers
Morgan         Coweta              McMinn             LOUISIANA PARISHES               Mayes
Jackson        Dekalb              Polk               ------------------               Wagoner
Limestone      Douglas             Rhea               St. John         Franklin        Muskogee
Montgomery     Fayette             Roane              Ascension        Richland        Cherokee
Bibb           Fulton              Scott              Jefferson        Ouachita        Craig
Coosa          Gwinnett            Sequatchie         Plaquemine       Morehouse       Adair
Elmore         Henry               Van Buren          Livingston       Claiborne       Delaware
Dallas         Paulding            Warren             Caldwell         Orleans         Ottawa
Pike           Rockdale            Bedford            St. Martin       Jackson         Nowata
Macon          Spalding            Cannon             Lafayette        St. Bernhard    Sequoyah
Crenshaw       Barrow              Coffee             Vermillion       St. Charles     Leflore
Green          Dawson              Franklin           Iberia           Bienville       McIntosh
               Forsyth             Giles              Acadia           Tensas          Haskell
VIRGINIA       Hall                Lincoln            St. Landry       Catahoula
COUNTIES       Jackson             Marshall           Evangeline       Madison
--------       Lumpkin             Moore              St. Mary         East Carroll
Lee            Banks               Rutherford         Jefferson Davis  West Carroll
Scott          Elbert              Cheatum            Allen            Union
Wise           Franklin            Davidson           Pointe Coupee    Lincoln
Dickinson      Habersham           Macon              Terrebonne       Concordia
Russell        Hart                Maury              Assumption       St. Tammany
Tazewell       Madison             Montgomery         Beauregard       Bossier
Smythe         Rabun               Robertson          Rapides          Caddo
Washington     Stephens            Rutherford         Avoyelles        Calcasieu
               Catoosa             Smith              Winn             Cameron
               Chatooga            Sumner             Vernon           St. Helena
               Dade                Trousdale          Grant            Red River
               Gordon              Wilson             Tangipahoa       Webster
               Murray              Williamson         Natchitoches
               Walker              Washington         LaSalle
               Whitfield           Carter             East Baton Rouge
               Floyd               Johnson            West Baton Rouge
               Polk                Unicoi             East Feliciana
                                   Hawkins            West Feliciana
                                   Greene             St. James
                                   Sullivan           Iberville
                                   Dickson            Lafourche
                                   Hickman
                                   Houston
</TABLE>

<PAGE>   9
<TABLE>
<CAPTION>

TEXAS COUNTIES                          FLORIDA COUNTIES
--------------                          ----------------

<S>                <C>                  <C>
Collin             Frio                 Pinellas
Kaufman            Gillespie            Pasco
Montague           Goliad               Citrus
Comanche           Gonzales             Manatee
Cooke              Nolan                Sarasota
Dallas             Nueces               DeSoto
Denton             Refugio              Hillborough
Ellis              Starr                Hardee
Erath              Taylor               Charlotte
Fannin             Hays                 Lee
Gray               Hildago              Highlands
Grayson            Jones                Hernando
Navarro            Travis               Sumpter
Palo Pinto         Uvalde               Lake
Parker             Victoria             Polk
Rockwall           Williamson           Orange
Rusk               Wilson
Sherman            Zevala
Tarrant            De Witt
Terrell            Duval
Henderson          Fisher
Hood
Hopkins
Johnson
Tyler
Van Zandt
Wise
Atascosa
Austin
Austin-San Antonio Corridor
Bandera
Bell
Bexar
Blanco
Burnet
Caldwell
Calhoun
Callaban
Cameron
Karnes
Kendall
Levaca
Lee
Live Oak
Llano
Mason
McMullen
Medina
Milam
Corvell
</TABLE>

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