<PAGE>   1
                                                                 EXHIBIT 10.1.1


      TAPPAN ZEE FINANCIAL, INC. 1996
              STOCK OPTION PLAN
         FOR OFFICERS AND EMPLOYEES

         (Adopted on March 25, 1996
       Effective as of July 11, 1996)


                  AMENDMENT


1.    Article II - Effective as of July 11, 1996, section 2.3(e) shall be 
amended by replacing the word "FInancial" with the word "Financial" where the
latter word appears therein.


2.   Article II - Effective as of July 11, 1996, Article II shall be amended by
deleting section 2.15 therefrom and redesignating all remaining sections of
Article II and all cross-references thereto accordingly.


3.   Article II - Effective as of July 11, 1996, section 2.23 shall be amended
by by replacing the word "Suprevision" with the word "Supervision" each time the
latter word appears therein.


4.   Article IV - Effective as of July 11, 1996, Article IV shall be amended by
deleting section 4.9 therefrom and redesignating the remaining section of
Article IV and all cross-references thereto accordingly.


5.   Article IV - Effective as of July 11, 1996, section 4.9, as redesignated,
shall be amended as follows: first, the phrase "at any time prior to October 5,
1996," shall be deleted from subsection (b) and second, the first clause in
subsection (c) shall be amended and restated to read:

         (c)      each Option granted under the Plan shall become exercisable as
                  follows:


6.    Article IV - Effective as of July 11, 1996, section 5.3 shall be amended 
and restated in its entirety to read as follows:


                                   Page 1 of 3

<PAGE>   2




         SECTION 5.3     ADJUSTMENTS IN THE EVENT OF A BUSINESS REORGANIZATION.

                  (a)    In the event of any merger, consolidation, or other
         business reorganization in which the Company is the surviving entity,
         and in the event of any stock split, stock dividend or other event
         generally affecting the number of Shares held by each Person who is
         then a holder of record of Shares, the number of Shares covered by each
         outstanding Option and the number of Shares available pursuant to
         section 4.2 shall be adjusted to account for such event. Such adjust
         ment shall be effected by multiplying such number of Shares by an
         amount equal to the number of Shares that would be owned after such
         event by a Person who, immediately prior to such event, was the holder
         of record of one Share, and the Exercise Price of the Options shall be
         adjusted by dividing the Exercise Price by such number of Shares;
         provided, however, that the Committee may, in its discretion, establish
         another appropriate method of adjustment.

                  (b)    In the event of any merger, consolidation, or other
         business reorganization in which the Company is not the surviving
         entity, any exercisable Options granted under the Plan which remain
         outstanding may be cancelled as of the effective date of such merger,
         consolidation, business reorganization, liquidation or sale by the
         Board upon 30 days' written notice to the Option holder; provided,
         however, that on or as soon as practicable following the date of
         cancellation, each Option holder shall receive a monetary payment in
         such amount, or other property of such kind and value, as the Board
         determines in good faith to be equivalent in value to the Options that
         have been cancelled.

                  (c)    In the event that the Company shall declare and pay any
         dividend with respect to Shares (other than a dividend payable in
         Shares) which results in a nontaxable return of capital to the holders
         of Shares for federal income tax purposes or otherwise than by dividend
         makes distribution of property to the holders of its Shares, the
         Company shall, in the discretion of the Committee, either:

                           (i)     make an equivalent payment to each Person 
                  holding an outstanding Option as of the record date for such
                  dividend. Such payment shall be made at substantially the same
                  time, in substantially the same form and in substantially the
                  same amount per optioned Share as the dividend or other
                  distribution paid with respect to outstanding Shares;
                  provided, however, that if any dividend or distribution on
                  outstanding Shares is paid in property other than cash, the
                  Company, in the Committee's discretion, may make such payment
                  in a cash amount per optioned Share equal in fair market value
                  to the fair market value of the non-cash dividend or
                  distribution; or

                           (ii)    adjust the Exercise Price of each outstanding
                  Option in such manner as the Committee may determine to be
                  appropriate to equitably reflect the payment of the dividend;
                  or

                                   Page 2 of 3

<PAGE>   3


                           (iii)   take the action described in section 
                  5.3(c)(i) with respect to certain outstanding Options and the
                  action described in section 5.3(c)(ii) with respect to the
                  remaining outstanding Options;

         provided, however, that no such action shall be taken without the
         approval of the Office of Thrift Supervision until the stockholders of
         the Company have voted to approve the provisions of this section 5.3(c)
         in a vote taken after October 5, 1996.


7.   Article VI - Effective as of July 11, 1996, section 6.8 shall be amended as
follows: first, the first sentence in such section shall be amended by deleting
therefrom the words "and Limited Stock Appreciation Rights" and second, the
second sentence of section 6.8 shall be amended by deleting therefrom the words
"or Limited Stock Appreciation Rights" each time such words appear therein.

                                   Page 3 of 3