<PAGE>
 
                                                                    Exhibit 4.15

                             SUPPLEMENTAL INDENTURE
                                    between
                             EVEREST TWO IPA, INC.
                                      and
              AMERICAN NATIONAL BANK AND TRUST COMPANY OF CHICAGO

     SUPPLEMENTAL INDENTURE (this "Supplemental Indenture"), dated as of
December 1, 1998, between Everest Two IPA, Inc. (the "New Subsidiary
Guarantor"), a direct or indirect domestic Restricted Subsidiary of Everest
Healthcare Services Corporation (the "Company") and American National Bank and
Trust Company of Chicago, as trustee under the indenture referred to below (the
"Trustee").  Capitalized terms used herein and not defined herein shall have the
meaning ascribed to them in the Indenture (as defined below).

                              W I T N E S S E T H

     WHEREAS, the Company has heretofore executed and delivered to the Trustee
an indenture (the "Indenture"), dated as of May 5, 1998, providing for the
issuance of an aggregate principal amount of up to $150,000,000.00 of 9-3/4%
Senior Subordinated Notes due 2008 (the "Notes");

     WHEREAS, Section 4.10 of the Indenture provides that under certain
circumstances the Company may cause, and Section 4.20 of the Indenture provides
that under certain circumstances the Company must cause, certain of its
subsidiaries to execute and deliver to the Trustee a supplemental indenture
pursuant to which such subsidiaries shall unconditionally guarantee all of the
Company's Obligations under the Notes pursuant to a Guarantee on the terms and
conditions set forth herein; and

     WHEREAS, pursuant to Section 9.1 of the Indenture, the Trustee is
authorized to execute and deliver this Supplemental Indenture.

     NOW, THEREFORE, in consideration of the foregoing and for other good and
valuable consideration, the receipt of which is hereby acknowledged, the New
Subsidiary Guarantor and the Trustee mutually covenant and agree for the equal
and ratable benefit of the Holders of the Notes as follows:

     1.   AGREEMENT TO GUARANTEE.  The New Subsidiary Guarantor hereby agrees,
jointly and severally with all other Subsidiary Guarantors, to guarantee the
Company's Obligations under the Notes and the Indenture on the terms and subject
to the conditions set forth in Article XI and XII of the Indenture and to be
bound by all other applicable provisions of the Indenture.

     2.   NO RECOURSE AGAINST OTHERS.  No director, officer, employee or
stockholder, as such, of the Subsidiary Guarantor shall have any liability for
any obligations of the 
<PAGE>
 
Company or any Subsidiary under the Notes, any Guarantees, the Indenture or this
Supplemental Indenture or for any claim based on, in respect of, or by reason
of, such obligations or their creation. Each Holder by accepting a Note waives
and releases all such liability. The waiver and release are part of the
consideration for issuance of the Notes.

     3.   NEW YORK LAW TO GOVERN.  The internal law of the State of New York
shall govern and be used to construe this Supplemental Indenture.

     4.   COUNTERPARTS.  The parties may sign any number of copies of this
Supplemental Indenture.  Each signed copy shall be an original, but all of them
together represent the same agreement.

     5.   EFFECT OF HEADINGS.  The Section headings herein are for convenience
only and shall not affect the construction hereof.

     6.   THE TRUSTEE.  The Trustee shall not be responsible in any manner
whatsoever for or in respect of the validity or sufficiency of this Supplemental
Indenture or for or in respect of the correctness of the recitals of fact
contained herein, all of which recitals are made solely by the New Subsidiary
Guarantor.

     7.   EFFECT OF SUPPLEMENTAL INDENTURE. Except as amended by this
Supplemental Indenture, the terms and provisions of the Indenture shall remain
in full force and effect.
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed and attested, all as of the date first above
written.



EVEREST TWO IPA, INC.


By:  /s/ John B. Bourke
     ------------------

John B. Bourke, an authorized signatory
--------------                         
 


AMERICAN NATIONAL BANK AND TRUST COMPANY OF CHICAGO
as TRUSTEE


By:  /s/ Anjali Gottreich
     --------------------

Print Name: Anjali Gottreich
           -----------------

Title: Assistant Vice President
      -------------------------