Document:

<PAGE>   1
                                                                   EXHIBIT 4.2C

                      SECOND AMENDMENT TO RIGHTS AGREEMENT
                         OF MAXICARE HEALTH PLANS, INC.

        This Second Amendment to Rights Agreement (this "Second Amendment") of
Maxicare Health Plans, Inc., a Delaware corporation (the "Company") is entered
into as of June 6, 2000, by and between American Stock Transfer & Trust Company,
a New York corporation ("AST") and the Company.

        WHEREAS, the Company entered into a Rights Agreement with AST dated
February 24, 1998 (the "Rights Agreement"), as amended by the First Amendment to
the Rights Agreement dated October 9, 1998 (the "First Amendment"); and

        WHEREAS, in connection with a proposed equity financing for the Company,
the Board of Directors has approved the grant to the Company's shareholders on
June 26, 2000 (the "Record Date") of rights to purchase for $1.00 per share, 1.5
shares of the Company's common stock for each share of common stock owned by
such shareholders on the Record Date (the "Rights Offering"); and

        WHEREAS, the effectiveness of the Rights Offering is subject to approval
by the Company's shareholders of an amendment to its certificate of
incorporation increasing the number of authorized shares of the Company's common
stock from 40,000,000 to 80,000,000 at the Company's 2000 Annual Meeting of
Shareholders (the "Annual Meeting"); and

        WHEREAS, the Company has existing Net Operating Losses (the "NOLs") of
approximately $400,000,000 which the Board of Directors wishes to preserve
notwithstanding the effectiveness of the Rights Offering; and

        WHEREAS, the existing NOLs may be jeopardized if one or more entities
acquire five percent or more of the Company's common stock and the Rights
Offering is successfully consummated; and

        WHEREAS, in conjunction with the Rights Offering, the Board of Directors
has approved and authorized for approval by the Company's shareholders at the
Annual Meeting an amendment to the Company's certificate of incorporation which
would prohibit, without the approval of the Board of Directors, the transfer of
any shares of the Company's common stock: (i) to any existing holder of 5.0% or
more of the Company's common stock or (ii) which would cause such entity to own
5.0% or more of the Company's common stock (the "Restriction on Transfer
Amendment"); and

        WHEREAS, in order to insure that there are no ownership changes of the
Company's common stock prior to the Annual Meeting which would jeopardize the
NOLs in the event the Company goes forward with the Rights Offering, the
Company's Board of Directors has adopted resolutions further amending the Rights
Agreement as set forth below, with the intent that all such amendments shall be
effective from the date of this Second Amendment.

                                        1
<PAGE>   2
        NOW, THEREFORE, in consideration of the terms and conditions hereinafter
set forth, the parties hereby agree as follows:

        1. Term. The amendments set forth in this Second Amendment shall be in
effect from the date hereof.

        2. Original Rights Agreement and First Amendment. Except as expressly
amended herein, all of the terms and conditions of the Rights Agreement, as
amended by the First Amendment, shall remain in full force and effect and shall
not be modified or amended in any way.

        3. Amendments. The Rights Agreement, as amended by the First Amendment,
shall be further amended as follows:

           (a) Section 1(a). Section 1(a), the definition of "Acquiring Person,"
is hereby deleted in its entirety and replaced with the following:

               "(a) "ACQUIRING PERSON" shall mean any Person who or which,
together with all Affiliates and Associates of such Person, without the prior
approval of at least a majority of the Disinterested Directors (as hereinafter
defined), shall be the Beneficial Owner of 5.0% or more of the then outstanding
Common Shares (other than as a result of a Permitted Offer (as hereinafter
defined)) or was such a Beneficial Owner at any time after the date hereof,
whether or not such person continues to be the Beneficial Owner of 5.0% or more
of the then outstanding Common Shares. Notwithstanding the foregoing, (A) the
term "Acquiring Person" shall not include (i) the Corporation, (ii) any
Subsidiary of the Corporation, (iii) any employee benefit plan of the
Corporation or of any Subsidiary of the Corporation, (iv) any Person or entity
organized, appointed or established by the Corporation for or pursuant to the
terms of any such plan, (v) any Person, who or which together with all
Affiliates and Associates of such Person becomes the Beneficial Owner of 5.0% or
more of the then outstanding Common Shares as a result of the acquisition of
Common Shares directly from the Corporation, or (vi) any Grandfathered
Stockholder: provided, however, that if, (X) without the prior approval of at
least a majority of the Disinterested Directors, any Grandfather Stockholder
acquires additional Common Shares (other than Common Shares acquired directly,
or options or convertible securities to acquire Common Shares directly from the
Corporation) after the date hereof and such Grandfathered Stockholder's
Beneficial Ownership of Common Stock exceeds 5.0% of the Common Shares
outstanding or (Y) any Grandfathered Stockholder files a Schedule 13D with the
Securities and Exchange Commission disclosing that the Grandfather Stockholder
now holds the Common Shares with any purpose, or with the effect of, changing or
influencing the control of the Corporation, or in connection with or as a
participant in any transaction having such purpose or effect, including any
transaction under Rule 13d-3(b) under the Securities Exchange Act of 1934 (the
"EXCHANGE ACT") and such Grandfather Stockholder's Beneficial Ownership of
Common Shares equals 5.0% or more, then such Grandfathered Stockholder shall
become an Acquiring Person, and (B) no Person shall be deemed to be an
"Acquiring Person" either (X) as a result of the acquisition of Common Shares by
the Corporation which, by reducing the number of Common Shares outstanding,

                                       2
<PAGE>   3

increases the proportional number of shares beneficially owned by such Person
together with all Affiliates and Associates of such Person; except that if (i) a
Person would become an Acquiring Person (but for the operation of this subclause
(X)) as a result of the acquisition of Common Shares by the Corporation, and
(ii) after such share acquisition by the Corporation, such Person, or an
Affiliate or Associate of such Person, becomes the Beneficial Owner of any
additional Common Shares, then such Person shall be deemed an Acquiring Person,
or (Y) if (i) within 5 business days after such Person would otherwise have
become an Acquiring Person (but for the operation of this subclause (Y)), such
Person notifies the Board of Directors that such Person did so inadvertently and
(ii) within the latter of (a) 2 Business Days after such notification or (b) 20
Business Days after such notification unless the Disinterested Directors
notifies such Person in writing that they have determined (which determination
may be based on any public statement or filing of such Person) that such Person
acquired the Common Shares with the purpose, or with the effect of, changing or
influencing the control of the Corporation, or in connection with or as a
participant in any transaction having such purpose or effect, including any
transaction under Rule 13d-3(b) under the Exchange Act, such Person is the
Beneficial Owner of less than 5.0% of the outstanding Common Shares.

           (b) Section 1(l). Section 1(l), the definition of "Grandfathered
Stockholder," is hereby amended to delete all the language following the word
"than" and to replace such deleted language with the following:

               "5.0% of the Common Shares."

           (c) Section 3(c). The Certificate Legend set forth in Section 3(c) is
hereby amended to delete the first sentence of the Certificate Legend and
replace such deleted language with the following:

               "This certificate also evidences and entitles the holder hereof
to certain rights as set forth in a Rights Agreement between Maxicare Health
Plans, Inc. and American Stock Transfer Corporation, dated as of February 24,
1998, as amended by the First Amendment to Rights Agreement dated October 9,
1998 and the Second Amendment to Rights Agreement dated June 6, 2000 (as
amended, the "Rights Agreement"), the terms of which, as amended, are hereby
incorporated herein by reference and a copy of which is on file at the principal
executive offices of Maxicare Health Plans, Inc."

           (d) Section 4(b). The Certificate Legend set forth in Section 4(b) is
hereby amended to delete the first sentence of the Certificate Legend and
replace such deleted language with the following:

               "The Rights represented by this Right Certificate are or were
beneficially owned by a Person who was or became an Acquiring Person or an
Affiliate or Associate of an Acquiring Person (as such terms are defined in the
Rights Agreement between Maxicare Health Plans, Inc. and American Stock Transfer
Corporation, dated as of February 24, 1998, as amended by the First Amendment to
Rights Agreement dated October 9, 1998 and the Second Amendment to Rights
Agreement dated June 6, 2000)."

                                       3
<PAGE>   4

           (e) Section 23(a)(ii). Section 23(a)(ii) is hereby amended to delete
the number "15%" deleted and replace such number with the following:

               "5.0%"

           (f) Exhibit B -- Form of Right Certificate. The Form of Right
Certificate, as set forth in Exhibit B, is hereby amended to delete the first
sentence of the first paragraph (which sentence begins with the words "This
certifies that") and replace such deleted language with the following:

               "This certifies that __________________, or registered assigns,
is the registered owner of the number of Rights set forth above, each of which
entitles the owner thereof, subject to the terms, provisions and conditions of
the Rights Agreement between Maxicare Health Plans, Inc., a Delaware corporation
(the "Corporation") and American Stock Transfer & Trust Company, a New York
corporation (the "Rights Agent"), dated as of February 24, 1998, as amended by
the First Amendment to Rights Agreement dated October 9, 1998 and the Second
Amendment to Rights Agreement dated June 6, 2000 (as amended, the "Rights
Agreement"), to purchase from the Corporation at any time after the Distribution
Date (as such term is defined in the Rights Agreement) and prior to 5:00 P.M.,
New York time, on February 23, 2008, unless the Rights evidenced hereby shall
have been previously redeemed by the Corporation, at the principal office or
offices of the Rights Agent designated for such purpose, or at the office of its
successor as Rights Agent, one five-hundredths of a fully paid non-assessable
share of Series B Preferred Stock, $0.01 par value per share (the "Preferred
Shares"), of the Corporation, at a purchase price of $45.00 per one
five-hundredths of Preferred Share (the "Purchase Price"), upon presentation and
surrender of this Right Certificate with the Form of Election to Purchase duly
executed."

           (g) Exhibit B -- Form of Assignment. The Form of Assignment, as set
forth in Exhibit B, is hereby amended to delete the sentence that begins with
the words "The undersigned hereby certifies" and replace such deleted language
with the following:

               "The undersigned hereby certifies that (1) the Rights evidenced
by this Right Certificate are not being sold, assigned or transferred by or on
behalf of a Person who is or was an Acquiring Person or an Affiliate or
Associate thereof (as such terms are defined in the Rights Agreement between
Maxicare Health Plans, Inc. and American Stock Transfer Corporation, dated as of
February 24, 1998, as amended by the First Amendment to Rights Agreement dated
October 9, 1998 and the Second Amendment to Rights Agreement dated June 6, 2000
(as amended, the "Rights Agreement")) and (2) after due inquiry and to the best
knowledge of the undersigned, the undersigned did not acquire the Rights
evidenced by this Right Certificate from any Person who is or was an Acquiring
Person or an Affiliate or Associate thereof (as such terms are defined in the
Rights Agreement)."

                                       4
<PAGE>   5

           (h) Exhibit B -- Form of Election to Purchase. The Form of Election
to Purchase, as set forth in Exhibit B, is hereby amended to delete the sentence
that begins with the words "The undersigned hereby certifies" and replace such
deleted language with the following:

               "The undersigned hereby certifies that (1) the Rights evidenced
by this Right Certificate are not being sold, assigned or transferred by or on
behalf of a Person who is or was an Acquiring Person or an Affiliate or
Associate thereof (as such terms are defined in the Rights Agreement between
Maxicare Health Plans, Inc. and American Stock Transfer Corporation, dated as of
February 24, 1998, as amended by the First Amendment to Rights Agreement dated
October 9, 1998 and the Second Amendment to Rights Agreement dated June 6, 2000
(as amended, the "Rights Agreement")) and (2) after due inquiry and to the best
knowledge of the undersigned, the undersigned did not acquire the Rights
evidenced by this Right Certificate from any Person who is or was an Acquiring
Person or an Affiliate or Associate thereof (as such terms are defined in the
Rights Agreement)."

               (i) Exhibit C -- Summary of Rights to Purchase Preferred Shares.
The Summary of Rights to Purchase Preferred Shares, as set forth in Exhibit C,
is hereby amended in the following particulars:

                   (i) The last sentence of the first paragraph (which sentence
begins with the words "The description and terms") is hereby deleted and
replaced with the following:

                       "The description and terms of the Rights are set forth in
a Rights Agreement between the "Corporation" and American Stock Transfer & Trust
Company, a New York corporation (the "Rights Agent"), dated as of February 24,
1998, as amended by the First Amendment to Rights Agreement dated October 9,
1998 and the Second Amendment to Rights Agreement dated June 6, 2000 (as
amended, the "Rights Agreement")."

                   (ii) The words "15% or more" in the second sentence of the
second paragraph are hereby deleted and replaced with the following:

                        "5.0% or more"

                   (iii) The number "15%" in the last sentence of the second
paragraph is hereby deleted and replaced with the following:

                         "5.0%"

        IN WITNESS WHEREOF, the undersigned parties have executed this Second
Amendment of the Rights Agreement as of the 6th day of June, 2000.

                                       5
<PAGE>   6

                                             MAXICARE HEALTH PLANS, INC
                                             a Delaware corporation

                                             /s/ PAUL R. DUPEE, JR.
                                             ----------------------------------
                                             By: Paul R. Dupee, Jr.,
                                                 Chief Executive Officer

                                             AMERICAN STOCK TRANSFER &
                                             TRUST COMPANY

                                             /s/  HERBERT J. LEMMER
                                             ----------------------------------
                                             By: Herbert J. Lemmer,
                                                 Vice President

                                       6<PAGE>   1

                                                                     EXHIBIT 4.3

FORM OF RIGHTS SUBSCRIPTION CERTIFICATE

  ---------                                                            ---------
    NUMBER                                                               RIGHTS
  ---------                                                            ---------

             THIS SUBSCRIPTION CERTIFICATE WILL BE VALUELESS IF NOT
       RECEIVED BY THE SUBSCRIPTION AGENT BEFORE 5:00 P.M., NEW YORK TIME
                             ON ______________, 2000

                         RIGHTS SUBSCRIPTION CERTIFICATE

                           MAXICARE HEALTH PLANS, INC.

                                                      CUSIP NO. ________________

THIS RIGHTS SUBSCRIPTION CERTIFICATE IS NOT TRANSFERABLE.

The terms and conditions of this rights offering are set forth in the Prospectus
relating to the offer by Maxicare Health Plans, Inc. (the "Company") of
non-transferable subscription rights to purchase ("Rights") up to 28,088,072
shares of common stock, $.01 par value per share ("Shares") of the Company dated
__________, 2000 and are incorporated herein by reference.

--------------------------------------------------------------------------------

                       SUBSCRIPTION PRICE: $1.00 PER SHARE

    (The number of rights you are entitled to is listed on the label below.)

RECORD HOLDER:

--------------------------------------------------------------------------------

The Rights represented by this Rights Subscription Certificate, in whole or in
part, may be exercised by completing Sections 1 and 2. Before exercising Rights,
Rights holders are urged to read the Prospectus carefully and in its entirety.
Copies of the Prospectus are available from the Company and American Stock
Transfer (the "Subscription Agent").

IMPORTANT - Complete the appropriate SECTION and delivery instructions, and SIGN
on reverse side. Subject to the provisions of the Prospectus, if the
instructions of the person completing this Rights

<PAGE>   2

Subscription Certificate are insufficient to delineate the proper action to be
taken with respect to all of the Rights evidenced hereby, such action as is
clearly delineated in such instructions will be taken.

THE RIGHTS REPRESENTED BY THIS RIGHTS SUBSCRIPTION CERTIFICATE MAY BE EXERCISED
(I) ONLY BY THE RECORD HOLDER OF THE COMPANY'S SHARES AS OF THE CLOSE OF
BUSINESS ON SEPTEMBER 14, 2000, OR BY SOMEONE DESIGNATED BY THE RECORD HOLDER AS
THE BENEFICIAL OWNER OF THE SHARES AND (II) ONLY IF THE PERSON EXERCISING SUCH
RIGHTS HAS RECEIVED A COPY OF THE PROSPECTUS. BY EXERCISING THE RIGHTS THE
HOLDER ACKNOWLEDGES RECEIPT OF THE PROSPECTUS. ACCORDINGLY, BY COMPLETING THIS
RIGHTS SUBSCRIPTION CERTIFICATE, YOU CERTIFY THAT AS OF THE CLOSE OF BUSINESS ON
SEPTEMBER 14, 2000, YOU ARE THE RECORD HOLDER OF _________ SHARES OF THE
COMPANY'S COMMON STOCK OR THAT YOU HAVE BEEN DESIGNATED BY THE RECORD HOLDER (IN
WRITING AS ATTACHED HERETO) AS THE BENEFICIAL OWNER OF SUCH SHARES ENTITLED TO
SUBSCRIBE TO __________ SHARES IN THIS RIGHTS OFFERING.

The Rights entitle the record or beneficial holder, as the case may be, to
subscribe for one and one-half shares of common stock of the Company at a
Subscription Price of $1.00 per Share for each Right evidenced hereby under the
terms and subject to the conditions set forth in the Prospectus. Payment of the
full Subscription Price for all Shares subscribed for pursuant to the exercise
of Rights must accompany this properly completed and duly executed Rights
Subscription Certificate, payable in United States currency by personal check,
cashier's check, bank draft or money order drawn on a bank located in the United
States, payable to "American Stock Transfer & Trust Company." PLEASE WRITE YOUR
RIGHTS CERTIFICATE NUMBER, SET FORTH ABOVE, ON YOUR CHECK, BANK DRAFT OR MONEY
ORDER.

Dated: _____________, 2000

                                             MAXICARE HEALTH PLANS, INC.

                                    By:_________________________________________
                                             Richard A. Link, Chief Operating
                                             Officer and Chief Financial Officer

                                    By: ________________________________________
                                             Alan D. Bloom, Secretary

INSTRUCTIONS: To exercise all or part of the Rights evidenced by this Rights
Subscription Certificate, please complete Section 1. In order to have the
Subscription Agent deliver Shares issued upon the exercise of Rights to another
person or delivered to an address other than the one listed on the face of this
Rights Subscription Certificate, please complete Section 2 and obtain the
required signature guarantee by a medallion institution.

YOUR EXERCISE OF RIGHTS IS IRREVOCABLE ONCE YOU HAVE SUBMITTED THIS RIGHTS
SUBSCRIPTION CERTIFICATE TO AMERICAN STOCK TRANSFER & TRUST COMPANY AS
SUBSCRIPTION AGENT. HOWEVER, THE COMPANY RESERVES THE RIGHT TO POSTPONE, MODIFY
OR CANCEL THE RIGHTS OFFERING AT ANY TIME PRIOR TO THE EXPIRATION OF THE THIRTY
DAY PERIOD OF THE RIGHTS OFFERING IF IT DETERMINES THAT SUCH POSTPONEMENT,
MODIFICATION OR CANCELLATION IS IN THE BEST INTERESTS OF MAXICARE HEALTH PLANS,
INC. AND ITS SHAREHOLDERS.

<PAGE>   3

SECTION 1 - EXERCISE AND SUBSCRIPTION: The undersigned hereby exercises Rights
to subscribe for Shares as indicated below, on the terms and subject to the
conditions specified in the Prospectus. By completing this Rights Subscription
Certificate, the undersigned hereby certifies that he/she has received and had
an opportunity to read the Prospectus dated _______, 2000.

(PLEASE PRINT ALL INFORMATION CLEARLY AND LEGIBLY)

        (i)    IF YOU WISH TO EXERCISE ALL OF YOUR RIGHTS:

               I subscribe for my full entitlement of Shares:

               _______________________ X $1.00 = $__________________
               (Number of shares held
                       times 1.5)

               TOTAL BASIC SUBSCRIPTION PRICE:     $________________
               (Total number of Shares subscribed
               for times the Subscription Price of
               $1.00 per share, rounded upward to
               the nearest whole number)

Method of Payment (check one)

[ ]     Check, Bank Draft or Money Order Payable to American Stock Transfer &
        Trust Company.

[ ]     Wire Transfer Directly to the account maintained by American Stock
        Transfer & Trust Company, at [Bank], ABA ROUTING #___________, for
        Credit Account #________, Further credit: MAXICARE RIGHTS OFFERING,
        Attn: ____________, [Phone]

        (ii)   IF YOU DO NOT WISH TO EXERCISE ALL OF YOUR RIGHTS:

               I subscribe for only

               _______________________________________ X $1.00 = $____________
               (Number of shares - whole number only)

               TOTAL SUBSCRIPTION PRICE:           $________________
               (Total number of Shares subscribed
               for times the Subscription Price
               of $1.00 per share)

Method of Payment (check one)

[ ]     Check, Bank Draft or Money Order Payable to American Stock Transfer as
        Subscription Agent.

[ ]     Wire Transfer Directly to the account maintained by American Stock
        Transfer & Trust Company, at [Bank], ABA ROUTING #___________, for
        Credit Account #________, Further credit: MAXICARE RIGHTS OFFERING,
        Attn: ____________, [Phone]

<PAGE>   4

SECTION 2 - SPECIAL INSTRUCTIONS [ ] CHECK HERE FOR SPECIAL ISSUANCE,OR DELIVERY
INSTRUCTIONS. Unless otherwise indicated below, the Subscription Agent is hereby
authorized to issue and deliver Certificates for the Shares subscribed for to
the undersigned at the address appearing on the face of this Rights Subscription
Certificate. If this section is completed, the Holder's signature must be
guaranteed by a medallion guarantor.

                      Name:         _____________________________________

                      Address:      _____________________________________

                                    _____________________________________

                      Taxpayer Identification or Social Security
                      Number:_____________________________________

                              IMPORTANT: RIGHTS HOLDER SIGN HERE

--------------------------------------------------------------------------------
 (Signature(s) of Holder(s) exactly as appears on the face of this Certificate)

Dated: ____________, 2000

SIGNATURE GUARANTEE (to be executed if Section 2 is completed)

The undersigned, an eligible guarantor institution pursuant to Rule 17Ad-15
promulgated under the Securities Exchange Act of 1934, as amended, and a
participant in a Securities Transfer Association recognized signature program,
does hereby guarantee that the signature of the Holder hereinabove is genuine.

Dated: ____________, 2000

                                            ------------------------------------
                                            Firm Name (If applicable)

                                            ------------------------------------
                                            Authorized Signature

                                            ------------------------------------
                                            Name and Title

                                            ------------------------------------
                                            Address

<PAGE>   5

                                            ------------------------------------

                                            ------------------------------------
                                            Area Code and Telephone Number

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00012-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00012-of-00352.parquet"}]]