<PAGE>   1


                                  EXHIBIT 4.3




                                      45
<PAGE>   2



                      AMENDMENT NO. 2 TO RIGHTS AGREEMENT

         THIS AGREEMENT No. 2 (the "Agreement"), dated as of January 16, 1997,
is between Studio Plus Hotels, Inc., a Virginia corporation (the "Company"),
and FIFTH THIRD BANK, as Rights Agent (the "Rights Agent")

                                    Recitals

                            A. The Company and the Rights Agent are parties to
an Amended and Restated Rights Agreement dated as of June 6, 1995, as amended
on February 27, 1996 (the "Rights Agreement").

                            B. Extended Stay America, Inc., a Delaware
corporation ("Merger Partner"), ESA Merger Sub. Inc., a Delaware corporation
and a wholly owned subsidiary of Merger Partner ("Merger Sub"), and the Company
propose to enter into an Agreement and Plan of Merger dated as of January 16,
1997 (the "Merger Agreement") pursuant to which the Company will be merged with
and into Merger Sub, with the Merger Sub as the surviving corporation (the
"Merger")

                            C. Pursuant to section 27 of the Rights Agreement,
the Board of Directors of the Company has determined that an amendment to the
Rights Agreement as set forth herein is necessary and desirable to reflect the
foregoing and certain other matters, and the Company and the Rights Agent
desire to evidence such amendment in writing.

                            Accordingly, the parties agree as follows:

                            1. Amendment of Section 1(a). Section 1(a) of the
Rights Agreement is amended by inserting the following at the end of Section
1(a):

                                    "In addition, notwithstanding anything in
                            this Rights Agreement to the contrary neither
                            Extended Stay America, Inc., a Delaware corporation
                            ("Merger Partner"), ESA Merger Sub, Inc., a Delaware
                            corporation and wholly owned subsidiary of Merger
                            Partner ("Merger Sub"), nor any Affiliate or
                            Associate of Merger Partner or Merger Sub, shall be
                            deemed to be an Acquiring Person by virtue of the
                            Agreement and Plan of Merger, to be entered into as
                            of January 16, 1997, between the Company, Merger
                            Partner and Merger Sub, as it may be amended or
                            supplemented from time to time in accordance with
                            its terms (the "Merger Agreement"), or by virtue of
                            any of the transactions contemplated by the Merger
                            Agreement, including without limitation, the
                            publication or other announcement of the Merger in
                            accordance with Section 5.6 of the Merger
                            Agreement."

                            2. Amendment of Section 1(k). Section 1(k) of the
Rights Agreement is amended by deleting the word "or" before the numeral (iii)
therein and by adding to the end thereof the following:

                            "or (iv) immediately prior to the Effective Time 
(as defined in



                                       46


<PAGE>   3



                           the Merger Agreement) of the Merger contemplated by
                           and in accordance with the terms of the Merger
                           Agreement."

                            3. Amendment of Section 3(a). Section 3(a) of the
rights Agreement is amended by adding the following sentence at the end thereof:

                                    "Notwithstanding the foregoing or anything
                           in this Rights Agreement to the contrary, a
                           Distribution Date shall not be deemed to have
                           occurred by virtue of the execution, consummation or
                           public announcement of the Merger Agreement or by
                           virtue of any of the transactions contemplated by
                           the Merger Agreement."

                            4. Amendment of Section 13. Section 13 of the
Rights Agreement is hereby amended by inserting the following sentence at the
end of such Section:

                                    "Notwithstanding the foregoing, this
                           Section 13 shall not apply to the Merger or as a
                           result of the execution and delivery of the Merger
                           Agreement or the transactions contemplated thereby."

                            5. Effectiveness. This Amendment shall be deemed
effective as of January 16, 1997, as if executed on such date. Except as
amended hereby, the Rights Agreement shall remain in full force and effect and
shall be otherwise unaffected hereby.

                            6. Miscellaneous. This Amendment shall be deemed to
be a contract made under the laws of the Commonwealth of Virginia and for all
purposes shall be governed by and construed in accordance with the laws of such
Commonwealth applicable to contracts to be made and performed entirely within
such Commonwealth. This Amendment may be executed in any number of
counterparts, each of such counterparts shall for all purposes be deemed to be
an original, and all such counterparts shall together constitute bu one and the
same instrument. If any term, provision, covenants or restriction of this
Amendment is held by a court of competent jurisdiction or other authority to be
invalid, void or unenforceable, the remainder of the terms, provisions,
covenants and restrictions of this Amendment shall remain in full force and
effect and shall in no way be affected, impaired or invalidated.



                                       47


<PAGE>   4



EXECUTED as of the date first set forth above.

                                      STUDIO PLUS HOTELS, INC.
Attest:                               a Virginia corporation

------------------------------        ---------------------------------
Name:                                 Name:
Title:                                Title:

Attest:                               FIFTH THIRD BANK, as Rights Agent


------------------------------        ---------------------------------
Name:                                 Name:
Title:                                Title:

                             

                                       48