<PAGE>
                                                                    EXHIBIT 10.4



                    (SSG CAPITAL ADVISORS, L.P. LETTERHEAD)




July 31, 2003



Judge Arlin M. Adams
Chapter 11 Trustee of Coram Healthcare Corporation
  and Coram, Inc.
Schnader Harrison Segal & Lewis, LLP
1600 Market Street, Suite 3600
Philadelphia, PA 19103-7286

Dear Judge Adams:

This agreement will serve as the first addendum ("First Addendum") to the
Engagement Agreement dated October 8, 2003 by and between the Chapter 11
Trustee ("Trustee") of Coram Healthcare Corporation and Coram, Inc. and SSG
Capital Advisors, L.P. ("SSG") and Ewing Bemiss & Co. ("EB") (collectively
"Advisor") in connection with Advisor's engagement as exclusive investment
banker and financial advisor to the Trustee, as approved by the Retention Order
dated December 2, 2002.

All defined terms that are capitalized in the Engagement Agreement remain in
place for this First Addendum with the following changes listed below:

1.   The Term is extended from July 9, 2003, the date of the expiration of the
     first Renewal Period, through December 9, 2003.

2.   In addition to the Monthly Fees, Advisor will be paid $100,000 per month
     for August, September, October and November, 2003 ("Additional Monthly
     Fees"). Because the Term has been extended and the scope of the Advisor's
     services has been expanded, the Additional Monthly Fees shall not be
     credited back against the Advisory Fee, the Minimum Advisory Fee or the
     Restructuring Fee.

3.   In the event that the Trustee and/or the Company requires an FASB 142
     Valuation for 2003, Advisor will be paid an additional $50,000, which shall
     not be credited back against the Advisory Fee, Minimum Advisory Fee or
     Restructuring Fee.

This First Addendum is subject to the approval of the United States Bankruptcy
Court for the District of Delaware after notice, which may be expedited, and an
opportunity for a hearing.

<PAGE>
  Judge Arlin M. Adams
  July 31, 2003
  Page 2

  Any further addendum, modification or other changes to the Engagement
  Agreement or this First Addendum must be in writing and signed by both
  parties to be enforceable.

  Please indicate your acceptance of the foregoing by executing and returning
  the enclosed copy of this First Addendum.

SSG CAPITAL ADVISORS, L.P.

By:  Chesen, DeMatteo, Karlson, Victor Securities Corporation,
     General Partner



By:  /s/ Mark E. Chesen                 /s/ J. Scott Victor
     ----------------------------       -------------------------------
     Mark E. Chesen                     J. Scott Victor
     President                          Managing Director


EWING BEMISS & CO.



By:  /s/ Samuel M. Bemiss               /s/ Michael S. Weber
     ----------------------------       -------------------------------
     Samuel M. Bemiss                   Michael S. Weber
     Managing Director                  Managing Director


ACCEPTED:

JUDGE ARLIN M. ADAMS, CHAPTER 11 TRUSTEE
CORAM HEALTHCARE CORPORATION AND CORAM, INC.




By:  /s/ Arlin M. Adams
     ----------------------------       -------------------------------
     Judge Arlin M. Adams               Date
     Chapter 11 Trustee