<PAGE>

                                                                    Exhibit 10.4
                                                                    ------------

          Amendment No. 1 to Research and Commercialization Agreement


     This Amendment No. 1 to Research and Commercialization Agreement (the
"Amendment") effective as of January ___, 1999, is entered into by and between
Schering AG ("Schering"), GenPharm International, Inc. and Medarex, Inc.
(collectively, "Medarex"), and amends that certain Research and
Commercialization Agreement entered into by Medarex and Schering effective as of
February 9, 1998 (the "Agreement").

1.   All capitalized terms not defined in this Amendment shall have the meanings
     given to them in the Agreement.

2.   Section 1.3 shall be amended to read in its entirety as follows:

     1.3  "Antigen" shall mean each of (i) [*****] as described in the Research
           -------
          Plan, (ii) any other antigen proposed by Schering and accepted by
          Medarex pursuant to Section 2.1.3.

3.   Section 1.16 shall be amended to read in its entirety as follows:

     1.16 "Product" shall mean any product for the diagnosis or treatment of
           -------
          human disease containing an Antibody or a portion thereof. A Product
          used for several indications is considered to be a single Product.

4.   Sections 2.1.1, 2.3, 2.4 and 2.7.2 are amended to change each reference to
     "the Antigen" to "each Antigen".

5.   Section 2.1.2. shall be revised by the addition of the following new last
     sentence:

     Medarex may, at its sole discretion, with notice to Schering discontinue
     any Research Program activities for which Schering is not providing full
     research support pursuant to Section 2.2. Within [*****] of such notice,
     Schering shall notify Medarex whether Schering wishes to provide research
     funding pursuant to Section 2.2 for the activities which Medarex intends to
     continue. Unless Schering timely notifies Medarex that Schering will
     provide full research funding for such activities, Medarex shall have the
     right to discontinue any or all of such activities.


***** REPRESENTS CONFIDENTIAL PORTION WHICH HAS BEEN OMITTED AND FILED
SEPARATELY WITH THE SECURITIES AND EXCHANGE COMMISSION. CONFIDENTIAL TREATMENT
HAS BEEN REQUESTED WITH RESPECT TO THE OMITTED PORTIONS.
<PAGE>

6.   Section 2.1 shall be amended by the addition of the following new Section
2.1.3:

     2.1.3   Selection of Antigens.  During the Research Program, Schering
             ---------------------
             may, with notice to Medarex, propose that one or more new antigens
             become Antigens subject to this Agreement. In each case, Schering
             shall notify Medarex of the identity of the proposed antigen and
             [*****]. Within [*****] after its receipt of any such proposal
             and information, Medarex shall notify Schering whether it will
             accept the proposed antigen as an Antigen. It is understood and
             agreed that Medarex shall have the right, at its sole discretion,
             to accept or refuse to accept any such proposed antigen as an
             Antigen. At such time as Medarex has accepted [*****] additional
             Antigens pursuant to this Section 2.1.3, Schering shall have no
             further right to propose additional Antigens, unless otherwise
             expressly agreed in writing by the parties.

7.   Section 2.5 shall be amended to read in its entirety as follows:

     2.5     Research License.  Medarex hereby grants to Schering the following
             ----------------
             licenses: [*****] license to use the Antibodies prepared by Medarex
             during the Research Period and for which Schering provided Research
             support payments pursuant to Section 2.2 [*****] solely for
             research and evaluation purposes, and [*****] license to use the
             Antibodies with specificity against any Antigen prepared by Medarex
             during the Research Period for which Schering did not provide
             Research support payments pursuant to Section 2.2. solely for
             research and evaluation purposes.

8.   Section 3.1.1 shall be amended to read in its entirety as follows:

     3.1.1   Option; Right of Negotiation.
             ----------------------------

                  (a)    During the Evaluation Period, Schering shall have (i)
             an exclusive option to obtain an exclusive (even as to Medarex),
             worldwide commercial license as set forth in Section 3.2 solely to
             develop Antibodies for which Schering provided Research support
             payments pursuant to Section 2.2 for use in the development and
             commercialization of Products, and (ii) a right of negotiation as
             set forth in Section 3.1.1(b) below to obtain an exclusive (even as
             to Medarex), worldwide commercial license as set forth in Section
             3.2 solely to develop Antibodies for which Schering did not provide
             Research support payments pursuant to Section 2.2 for use in the
             development and commercialization of Products. Schering may
             exercise such option by notice to Medarex during the foregoing
             period specifying [*****] to be covered


***** REPRESENTS CONFIDENTIAL PORTION WHICH HAS BEEN OMITTED AND FILED
SEPARATELY WITH THE SECURITIES AND EXCHANGE COMMISSION. CONFIDENTIAL TREATMENT
HAS BEEN REQUESTED WITH RESPECT TO THE OMITTED PORTIONS.

                                      -2-
<PAGE>

          by the commercial license, and concurrently paying to Medarex the
          applicable license fee due pursuant to Section 4.1.

               (b)  During the Evaluation Period, Schering shall have a right of
          negotiation to obtain a commercial license from Medarex with respect
          to any Antibodies prepared by Medarex for which Schering did not
          provide Research support payments to Medarex as follows: if during the
          Evaluation Period, a third party notifies Medarex that such third
          party wishes to acquire a commercial license to antibodies directed
          against such Antigen, or Medarex wishes to commercialize antibodies
          against such Antigen itself, Medarex shall notify Schering; however,
          Medarex shall not be obligated to identify such party, whether Medarex
          or a third party. If Schering has not notified Medarex within [*****]
          days of such notice that Schering will enter a commercial license for
          the Antibodies pursuant to Section 3.2 of this Agreement, then
          Schering's right of negotiation shall terminate with respect to the
          Antibodies and the related Antigen. In any such case, Medarex may
          grant one or more third parties commercial licenses with respect to
          antibodies specific for the applicable Antigen, or conduct
          commercialization of such antibodies itself.

               (c)  Medarex shall not license, sell, transfer or use in any
          manner any Antibodies arising out of the Research to any third party
          except Schering. At Schering's request, Medarex shall destroy any
          Antibodies, and related Mice Materials prepared by Medarex in the
          Research. Notwithstanding the above, it is understood and agreed that
          Medarex shall have no obligation to destroy any antibodies and related
          Mice Materials for which Schering did not provide research support
          payments pursuant to Section 2.2.

9.   Section 3.2 shall be amended to read in its entirety as follows:

     3.2  Commercial License.  Effective upon Schering's election to acquire a
          ------------------
          commercial license, subject to the terms and conditions of this
          Agreement (including without limitation, the timely payment of the
          license fee due pursuant to Section 4.1) Medarex shall grant to
          Schering the following licenses, on an Antigen-by-Antigen basis:

          3.2.1     an exclusive (even as to Medarex), worldwide, non-
                    transferable (except as set forth in Section 14.3), royalty
                    bearing license under the Medarex Technology with the right
                    to sublicense, to use hybridomas delivered by Medarex to
                    Schering to make or have made Antibodies, and

***** REPRESENTS CONFIDENTIAL PORTION WHICH HAS BEEN OMITTED AND FILED
SEPARATELY WITH THE SECURITIES AND EXCHANGE COMMISSION. CONFIDENTIAL TREATMENT
HAS BEEN REQUESTED WITH RESPECT TO THE OMITTED PORTIONS.

                                      -3-
<PAGE>

          3.2.2     an exclusive (even as to Medarex), worldwide, non-
                    transferable (except as set forth in Section 14.3), royalty
                    bearing license under the Medarex Technology, with the right
                    to sublicense, to use Antibodies to make, have made, import,
                    have imported, use, offer for sale and sell Products.

10.  Except as specifically modified or amended hereby, the Agreement shall
     remain in full force and effect and, as modified or amended, is hereby
     ratified, confirmed and approved. No provision of this Amendment may be
     modified or amended except expressly in a writing signed by both parties
     nor shall any terms be waived except expressly in a writing signed by the
     party charged therewith. This Amendment shall be governed in accordance
     with the laws of California, without reference to or application of
     conflicts of laws principles.

11.  Section 15.17 shall be added to read in its entirety as follows:


          15.17  Affiliates. Each Party may perform its obligations hereunder
                 ----------
     personally or through one or more Affiliates, although each Party shall
     nevertheless be solely responsible for the performance of its Affiliates.
     Neither Party shall permit any of its Affiliates to commit any act
     (including any act of omission) which such Party is prohibited hereunder
     from committing directly.


     IN WITNESS WHEREOF, each of the parties has executed this Amendment as of
the date indicated on this Amendment.


SCHERING AG                                  MEDAREX, INC.


By: Prof. Dr. Guenter Stock                  By: /s/ Michael Appelbaum
    ------------------------------              ------------------------------

Name:_____________________________           Name:  Michael Appelbaum
                                                  ----------------------------

Title: /s/ G. Stock                          Title: Executive V.P.
      ----------------------------                 ---------------------------
      Member Executive Board of
      Directors


Date: 22nd April 1999                        Date: May 11, 1999
      ----------------------------                ----------------------------



SCHERING AG                                  GENPHARM INTERNATIONAL, INC.


By:  /s/J.F. Kapp                            By: /s/ Michael Appelbaum
   -------------------------------              ------------------------------

                                      -4-
<PAGE>

Name: Dr. J-F. Kapp                          Name: Michael Appelbaum
     -----------------------------                ----------------------------

Title: Head of Strategic Business            Title: President & C.O.O
      ----------------------------                 ---------------------------
       Unit Therapeutics
      ----------------------------

Date:  22nd April 1999                       Date: May 11, 1999
     -----------------------------                ----------------------------

                                      -5-