Exhibit 10.4

ANTIGENICS, INC.

Amendment of Rights with respect to Events of Default and Issuance of Other
Securities

RECITALS

WHEREAS, reference is made to the Senior Secured Convertible Notes issued on
October 30, 2006 (together with any senior secured convertible notes issued in
replacement or exchange thereof in accordance with the terms thereof and any
senior secured convertible notes issued to pay interest, the “2006 Notes” and
each a “2006 Note”), by Antigenics, Inc., a Delaware corporation (the “Company”)
to Ingalls & Snyder Value Partners L.P. (“Ingalls”) and Penrith LTD (“Penrith”,
and together with Ingalls, the “Investors”);

WHEREAS, pursuant to the Indenture, dated January 25, 2005, between the Company
and HSBC Bank USA, National Association, the Company issued $50.0 million of
5.25% Convertible Senior Notes due 2025 (the “2005 Notes”) in a private
placement;

WHEREAS, the Company desires, at any time and from time to time, to redeem and
repurchase up to $15,000,000 in aggregate principal amount of 2005 Notes, along
with accrued but unpaid interest, for cash, from certain holders thereof (the
“2005 Notes Redemption”);

WHEREAS, pursuant to Section 4(a)(ii) of the 2006 Notes, the 2005 Notes
Redemption will constitute an Event of Default (as defined in the 2006 Notes);

WHEREAS, pursuant to Section 4(b) of the 2006 Notes, the Investors will have
certain redemption rights upon the occurrence of the Event of Default that
results from the 2005 Notes Redemption (the “Event of Default Rights”);

WHEREAS, at any time and from time to time, the Company may issue and sell
shares of Company Common Stock (as defined in the 2006 Notes), Convertible
Securities (as defined in the 2006 Notes), Options (as defined in the 2006
Notes) or any combination thereof (collectively, the “New Securities”) through a
public offering or a private placement (each a “Replenishment Offering”);

WHEREAS, pursuant to Section 7(a) of the 2006 Notes, the Investors may have
certain anti-dilutive rights upon the Company’s issuance and sale of New
Securities through a Replenishment Offering (the “Anti-Dilutive Rights”) if the
Replenishment Offering constitutes a Dilutive Issuance (as defined in the 2006
Notes);

WHEREAS, the undersigned parties desire to permit the 2005 Notes Redemption
subject to the terms and conditions set forth herein without triggering the
Event of Default Rights;

WHEREAS, the undersigned parties desire to permit each Replenishment Offering
subject to the terms and conditions set forth herein without triggering the
Anti-Dilutive Rights;

WHEREAS, pursuant to Section 15 of the 2006 Notes, the terms of the 2006 Notes
may be changed or amended by either (i) the affirmative vote at a meeting duly
called for such purpose or (ii) the written consent without a meeting, of the
holders of 2006 Notes representing at least a majority of the aggregate
principal amount of the 2006 Notes then outstanding; and

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WHEREAS, Ingalls holds 2006 Notes representing 80% of the aggregate principal
amount of the 2006 Notes outstanding;

NOW, THEREFORE, in consideration of the promises and agreements set forth in
this Amendment of Rights with respect to Events of Default and Issuance of Other
Securities (this “Amendment”), the undersigned agree as follows:

AGREEMENT

 

1. Definitions.    Capitalized terms used in this Amendment without definition
shall have the meanings ascribed to them in the 2006 Notes.

 

2. Amendment.

 

  a. The parties hereto hereby amend the Event of Default Rights by excluding
the 2005 Note Redemption from the definition of an Event of Default in
Section 4(a)(ii) of the 2006 Notes, subject to the condition that, in connection
with the 2005 Note Redemption, redemptions or repurchases by the Company of 2005
Notes be at a purchase price that does not exceed the sum of (i) twenty-five
percent (25%) of the outstanding principal of such notes plus (ii) the accrued
but unpaid interest on such notes.

 

  b. The parties hereto hereby amend Section 7(a) of the 2006 Notes by excluding
each Replenishment Offering from the definition of a Dilutive Issuance, subject
to the following conditions:

 

  i. If the New Issuance Price for such Replenishment Offering is less than
$1.00 per share, then (a) immediately after such Replenishment Offering, the
Fixed Conversion Price then in effect shall be reduced in the amount of the
difference between $1.00 per share and the New Issuance Price, and (b) for
purposes of determining the adjusted Fixed Conversion Price,
Section 7(a)(i)-(iv) of the 2006 Notes shall apply and “Applicable Price” shall
mean $1.00 per share with respect to such Replenishment Offering.

 

  ii. This section 2.b shall apply to up to an aggregate number of shares of
Company Common Stock (a) issued and sold through all Replenishment Offerings and
(b) available for issuance under Options and/or Convertible Securities sold
through all Replenishment Offerings, equal to ten percent (10%) of the total
number of shares of Company Common Stock issued and outstanding on the Business
Day immediately preceding the consummation of the Replenishment Offering in
question.

 

  iii. The aggregate dollar amount raised in the Replenishment Offerings is not
to exceed the aggregate dollar amount (excluding accrued but unpaid interest)
expended by the Company on any 2005 Note Redemptions.

 

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3. Miscellaneous.    Other than as specifically set forth herein, this Amendment
shall not be construed as a consent to any future action or an amendment of any
right or remedy on any future occasion. This Amendment may be executed in one or
more counterparts, all of which shall be considered one and the same amendment.

[Signature Page Follows]

 

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IN WITNESS WHEREOF, the undersigned have executed this Amendment as of November
    11    , 2008.

 

ANTIGENICS, INC. By:   /s/    Garo H. Armen Name:   Garo H. Armen, Ph.D. Title:
  Chairman & CEO INGALLS & SNYDER VALUE PARTNERS L.P. By:   /s/    Thomas O.
Boucher Name:   Thomas O. Boucher Title:   General Partner