<PAGE>
                                                                   Exhibit 10.19

                                                               Execution Version

                   AMENDMENT NO.2 TO ASSET PURCHASE AGREEMENT

     This Amendment No.2 to the Asset Purchase Agreement (this "Amendment No.2")
is entered into as of February 2, 2005, by and among SmithKline Beecham
Corporation (doing business as GlaxoSmithKline), a Pennsylvania corporation (the
"Buyer"), Corixa Corporation, a Delaware corporation ("Corixa"), Coulter
Pharmaceutical, Inc., a Delaware corporation and wholly-owned subsidiary of
Corixa ("Coulter"), (Corixa and Coulter being hereinafter collectively and/or
individually referred to, as the context requires and admits, as the "Sellers").
The Sellers, on the one hand, and the Buyer, on the other hand, are each
referred to herein as a "Party" and, collectively, as the "Parties."

                                    RECITALS

     WHEREAS, the Parties entered into that certain Asset Purchase Agreement
dated as of December 12, 2004 in connection with the Sellers' sale and the
Buyer's purchase of the Assets, as amended as of December 31, 2004 (the
"Agreement"); and

     WHEREAS, since the date of the Agreement's first amendment on December 31,
2004, the Parties have identified an additional employee of the Sellers who will
be participating in the Transition Plans as a Scheduled Employee.

                                    AGREEMENT

     NOW, THEREFORE, in consideration of the mutual agreements contained herein
and for other good and valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, and pursuant to Section 9.2 of the Agreement, the
Parties hereby agree as follows:

1.   SCHEDULED EMPLOYEES.

     Schedule 7.2 to the Agreement is hereby deleted in its entirety and
replaced with EXHIBIT A attached hereto.

2.   DEFINED TERMS.

     Capitalized terms that are used, but not otherwise defined, in this
Amendment No.2 shall have the meaning ascribed to them in the Agreement.

3.   GOVERNING LAW.

     This Amendment No.2 and all acts and transactions pursuant hereto shall be
governed, construed and interpreted in accordance with the Laws of the state of
New York, without giving effect to principles of conflict of Laws.

4.   COUNTERPARTS.

     This Amendment No.2 may be executed in two or more counterparts, each of
which shall be deemed an original and all of which together shall constitute one
instrument.

<PAGE>

5.   ENTIRE AGREEMENT.

     The terms of the Agreement, as amended hereby, shall remain in full force
and effect. All references to the "Agreement" contained therein shall mean the
Agreement, as amended on December 31, 2004 and further amended by this Amendment
No.2.

                            [signature page follows]


                                       -2-

<PAGE>

     IN WITNESS WHEREOF, this Amendment No.2 has been duly executed and
delivered by the duly authorized representatives of each Seller and the Buyer as
of the date first above written.

                                        THE BUYER:

                                        SMITHKLINE BEECHAM CORPORATION
                                        (D/B/A GLAXOSMITHKLINE)


                                        By: /s/ DONALD F. PARMAN
                                            ------------------------------------
                                            Name: Donald F. Parman
                                            Title: Vice President & Secretary

                                        THE SELLERS:


                                        CORIXA CORPORATION


                                        By: /s/ STEVEN GILLIS
                                            ------------------------------------
                                            Name: Steven Gillis
                                            Title: CEO


                                        COULTER PHARMACEUTICAL, INC.


                                        By: /s/ STEVEN GILLIS
                                            ------------------------------------
                                            Name: Steven Gillis
                                            Title: President