<PAGE>
 
                                                                     Exhibit 2.2
 
                                AMENDMENT NO. 1
                        TO AGREEMENT AND PLAN OF MERGER
                         Dated as of November 24, 1998


     TM Transitory Merger Corporation, a Michigan corporation ("BUYER"), TISM,
Inc., a Michigan corporation ("TISM") and Mr. Thomas S. Monaghan (the "PRINCIPAL
STOCKHOLDER"), individually and as trustee of The Thomas S. Monaghan Living
Trust, hereby agree as follows:

1.   Reference to the Merger Agreement; Definitions.  Reference is made to the
     ----------------------------------------------                           
     Agreement and Plan of Merger dated as of September 25, 1998 (as amended,
     the "Merger Agreement"), among Buyer, TISM and the Principal Stockholder.
     Terms defined in the Merger Agreement and not otherwise defined herein are
     used herein as so defined.

2.   Amendments to Merger Agreement.  The Merger Agreement is hereby amended as
     ------------------------------                                            
     follows:

     (a)  Amendments to Section 5.05.
          -------------------------- 

          (i)  Clause (ii) of the first sentence of Section 5.05 is hereby
               amended and restated so as to read in its entirety as follows:
               "(ii) (a) a commitment letter dated as of the date hereof from
               J.P. Morgan Securities Inc. ("JPMSI") pursuant to which JPMSI has
               committed, subject to the terms and conditions set forth or
               referred to therein, to purchase subordinated debt securities in
               the amount of $380,000,000 and (b) a preliminary offering
               memorandum dated on or about November 24, 1998 relating to an
               offering by Domino's, Inc. of $275,000,000 of Senior Subordinated
               Notes due 2008 (which contemplates the concurrent sale of
               $105,000,000 of Preferred Stock);" and

          (ii) The second sentence of Section 5.05 is hereby amended and
               restated so as to read in its entirety as follows:  "The
               aforementioned credit agreements and commitments to purchase debt
               and equity securities shall be referred to as the "FINANCING
               AGREEMENTS" and the financing described in clauses (i), (ii)(a)
               or (b), and (iii) shall be referred to as the "FINANCING.""

3.   Waiver under Merger Agreement.  Reference is made to the Amended and
     -----------------------------                                       
     Restated Retention Agreements with Patrick Doyle and Bob Fulmer (the
     "Amended and Restated Retention Agreements"), a copy of which has been
     furnished to Buyer.  The Buyer hereby waives the provisions of the Merger
     Agreement solely to the extent necessary to permit the execution and
     delivery of the Amended and Restated Retention Agreements.
<PAGE>
 
4.   Miscellaneous.  Except to the extent specifically amended or waived hereby
     -------------                                                             
     the provisions of the Merger Agreement have not been otherwise amended or
     waived, and the Merger Agreement as amended and waived hereby is hereby
     confirmed as being in full force and effect. This Amendment may be executed
     in any number of counterparts which together shall constitute one
     instrument, shall be governed by and construed in accordance with the law
     of the State of New York, without regard to the conflict of law rules of
     such state.  This Agreement shall become effective when each party hereto
     shall have received a counterpart hereof signed by each other party hereto.

     In WITNESS WHEREOF, the parties have executed and delivered this Amendment
or caused this Amendment to be executed and delivered by their duly authorized
officers as of the date first above written.

                              TM TRANSITORY MERGER CORPORATION


                              By: /s/ Andrew Balson
                                  --------------------------
                                  Name:  Andrew Balson
                                  Title: Vice President

                              TISM, INC.


                              By: /s/ Thomas S. Monaghan
                                  --------------------------
                                  Name:  Thomas S. Monaghan
                                  Title: Chairman and CEO


                              /s/ Thomas S. Monaghan
                              ------------------------------
                              THOMAS S. MONAGHAN
                              Individually and as Trustee

                                      -2-