<PAGE>

                                                                   Exhibit 10.31

                    AMENDMENT NO. 3 TO STOCKHOLDERS AGREEMENT

     This Amendment No. 3 to Stockholders Agreement (this "Amendment"), dated as
of December 1, 2002, by Concentra Inc., a Delaware corporation formerly known as
Concentra Managed Care, Inc. (the "Company"), and a majority in interest of each
of the Schedule I Purchasers and FFC Purchasers (each as hereinafter defined).
Capitalized terms used in this Amendment which are not otherwise defined herein
shall have the respective meanings assigned to them in the Stockholders
Agreement referred to below.

                                   WITNESSETH:

     WHEREAS, the Company is party to a certain Stockholders Agreement dated as
of August 17, 1999 (as amended, the "Stockholders Agreement"), together with the
several persons named on Schedule I thereto under the heading "Schedule I
Purchasers" (the "Schedule I Purchasers"), and the several persons named on
Schedule II thereto under the heading "FFC Purchasers" (the "FFC Purchasers"
and, together with the Schedule I Purchasers, collectively, the "Purchasers");
and

     WHEREAS, on November 1, 2001, the Company issued to certain of its existing
shareholders an aggregate 2,266,546 shares of Company Common Stock and warrants
to acquire an aggregate 771,277 additional shares of Company Common Stock and,
in connection therewith, the Stockholders Agreement was amended by Amendment No.
1 thereto dated as of November 1, 2001, to provide for certain matters relating
to such shares and such warrants; and

     WHEREAS, on November 20, 2002, the Company issued to certain of its
existing shareholders an aggregate 1,515,152 shares of Company Common Stock and,
in connection therewith, the Stockholders Agreement was amended by Amendment No.
2 thereto dated as of November 20, 2002, to provide for certain matters relating
to such shares; and

     WHEREAS, in connection with the Company's December 1, 2002, acquisition of
Em3 Corporation ("Em3"), the Company issued an aggregate 1,826,956 shares of
Company Common Stock to certain of its existing shareholders and to certain
former shareholders of Em3 who were not already shareholders of the Company, and
the Company wishes to afford to such new shareholders the opportunity to become
parties to the Stockholders Agreement as set forth herein; and

     WHEREAS, pursuant to Section XIII.(6) thereof, the Stockholders Agreement
can be amended as set forth in this Amendment by approval of the Company and
affirmative vote of a majority in interest of each of the Schedule I Purchasers
and FFC Purchasers;

     NOW, THEREFORE, in consideration of the foregoing and the mutual agreements
and covenants set forth herein and other good and valuable consideration, the
parties hereto agree as follows:

     1.   Amendment to Stockholders Agreement. Schedule I to the Stockholders
Agreement is hereby amended to include each of the persons set forth in Exhibit
A hereto

                                       1

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                                                                   Exhibit 10.32

"Joining Persons"), upon such Joining Persons' execution and delivery of a
Joinder Agreement substantially in the form attached hereto as Exhibit B.

     2.  Miscellaneous.

        (a) This Amendment shall be governed by and construed in accordance with
the laws of the State of New York.

        (b) This Amendment may be executed in two or more counterparts, each of
which shall be deemed an original, but all of which together shall constitute
one and the same instrument.

        (c) Headings and section reference numbers in this Amendment are for
reference purposes only and shall not in any way affect the meaning or
interpretation of this Amendment.

        (d) This Amendment is limited precisely as written and shall not be
deemed to be a modification, acceptance or waiver of any other term, condition
or provision of the Stockholders Agreement.

     IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of
the date first above written.

                                    CONCENTRA  INC.

                                    By: /s/ Richard A. Parr II
                                       ---------------------------------
                                        Richard A. Parr II
                                        Executive Vice President

         [Schedule I Purchaser and FFC Purchaser Signature Page Follows]

                                       2

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                                                                   Exhibit 10.32

Schedule I Purchasers:     WELSH, CARSON, ANDERSON & STOWE VIII, L.P.
                           By:   WCAS VIII Associates, L.L.C.,
                                 General Partner

                           By:   /s/ Jonathan M. Rather
                               --------------------------------------------
                                 Managing Member

                           WELSH, CARSON, ANDERSON & STOWE VI, L.P.
                           By:   WCAS VI ASSOCIATES, L.L.C.
                                 General Partner

                           By:   /s/ Jonathan M. Rather
                               --------------------------------------------
                                 Jonathan M. Rather
                                 Attorney-in-Fact

FFC Purchasers:            FERRER FREEMAN & COMPANY, LLC
                           on behalf of FFC PARTNERS I, L.P.
                           and as its General Partner

                           By:   /s/ Carlos A. Ferrer
                              ---------------------------------------------
                                 Carlos A. Ferrer
                                 Manager

                                                  and

                           on behalf of FFC EXECUTIVE PARTNERS I, L.P.
                           and as its General Partner

                           By:   /s/ Carlos A. Ferrer
                               --------------------------------------------
                                 Carlos A. Ferrer
                                 Manager

                                                  and

                           on behalf of FFC PARTNERS II, L.P.
                           and as its General Partner

                           By:   /s/ Carlos A. Ferrer
                               --------------------------------------------
                                 Carlos A. Ferrer
                                 Manager

                                       3

<PAGE>

                                                                   Exhibit 10.32

                                    EXHIBIT A

                                 Joining Parties

Michael Correia

Gary Zigenfus

William R. Winton

Eric Lee

Curtis J. Hoffman

Trudy Rios

Elijah C. Marentette

John K. Carlyle

Ken Wilkinson

Michael T. Fricke

Michael S. McCord

Kristan A. Covey

Ben Morgan

Geneva M. Giang

Mary P. Nixon

                                       A-1

<PAGE>

                                                                   Exhibit 10.32
                                    EXHIBIT B

                            Form of Joinder Agreement

                                JOINDER AGREEMENT

         This Joinder Agreement (the "Joinder") to the Amendment No. 3 to
Stockholders Agreement, dated as of August 17, 1999 (as amended, the
"Stockholders Agreement"), among Concentra Inc. (f/k/a Concentra Managed Care,
Inc.), a Delaware corporation ("Concentra"), and the several persons named in
Schedules I and II thereto, is executed and delivered by ________________ (the
"Joining Party") as of December 1, 2002. Each capitalized term used but not
otherwise defined herein shall have the meaning set forth in the Stockholders
Agreement.

         1. Agreement to be Bound. The Joining Party hereby agrees to be bound
by all of the terms of the Stockholders Agreement, attached to this Joinder as
Exhibit A (as the same may be hereafter amended, restated, or otherwise modified
from time to time). The Joining Party shall hereafter be deemed to be a
"Schedule I Purchaser" and a "Purchaser" for all purposes under the Stockholders
Agreement.

         2. Concentra Representations and Warranties. Each of the
representations and warranties of Concentra set forth in the Stockholders
Agreement is true and correct in all material respects as of the date hereof
with the same effect as though such representation and warranty had been made on
and as of this date.

         3. Joining Party Representations and Warranties. Each of the
representations and warranties of the Joining Party set forth in the
Stockholders Agreement is true and correct in all material respects as of the
date hereof with the same effect as though such representation and warranty had
been made on and as of this date.

         4. Notices. For purposes of notices and other communications to be
delivered to the Joining Party, the addresses and facsimile numbers set forth
below shall be deemed an amendment to Schedule I of the Stockholders Agreement
with respect to the Joining Party.

         5. Governing Law. This Joinder Agreement shall be governed by and
construed in accordance with the laws of the State of New York.

AGREED AND ACCEPTED:                   _________________________________________
                                          Signature of Joining Party

CONCENTRA INC.
                                      Print Name:_______________________________

By:_________________________          Address: _________________________________
    Richard A. Parr II
    Executive Vice President                   _________________________________

                                      Facsimile No:_____________________________

                                       B-1