<PAGE>

                                                                   EXHIBIT 10.32

                          SECOND AMENDMENT AGREEMENT
                          --------------------------

     THIS SECOND AMENDMENT AGREEMENT (the "Amendment") is made as of the 24th
day of May, 1996, by and between Lisle Property Venture, Inc., a Delaware
corporation ("LANDLORD") and Platinum Technology, Inc., a Delaware corporation
("TENANT").


                              W I T N E S S E T H
                              - - - - - - - - - -

     WHEREAS, LANDLORD and TENANT have heretofore made and entered into a lease
dated October 31, 1995 and if executed by LANDLORD, amended by a First Amendment
Agreement (the "First Amendment") dated May 23, 1996 (the "Lease"); and

     WHEREAS, LANDLORD and TENANT wish to add Space 2 (hereinafter described) to
the PREMISES subject to the terms hereof; and

     WHEREAS, the parties wish to modify the Lease.

     NOW, THEREFORE, in consideration of the premises, the Lease is amended as
follows:


                    MODIFICATION TO EXISTING TERMS OF LEASE
                    ---------------------------------------

     For the balance of the Term after August 1, 1996, the following changes are
made to the Lease:

          (a)  on August 1, 1996, the PREMISES is changed to add and include
     "Space 2" outlined on Appendix "A," which is located on the first of 650
     Warrenville Road.

          (b)  Beginning August 1, 1996, the rentable square feet of the
     PREMISES is increased by 7,758 square feet.

          (c)  Section 4B, for periods beginning November 11, 1996, the TENANT'S
PROPORTIONATE SHARE is increased by 4.49%.

          (d)  Section 5, the Annual Base Rent and Monthly Base Rent for the
Period after November 11, 1996 (Annual Base Rent and Monthly Base Rent for
partial years or months shall be prorated) shall be increased by the amounts in
the following schedule:
<PAGE>

<TABLE>
<CAPTION>
                         Increase to         Increase to         Net
                         Annual Base          Monthly           Rent
          Dates             Rent              Base Rent        PSF for
          -----           --------            ---------
                                                                Space
                                                                -----
<S>                      <C>                 <C>               <C>
  11/11/96-11/30/96                          $ 8,913.08*
       12/96-9/97        $160,435.44         $13,369.62          $20.68
         10/97           $161,606.64         $13,467.22          $20.83
       11/97-9/98        $163,461.12         $13,621.76          $21.07
         10/98           $164,662.32         $13,721.86          $21.22
       11/98-9/99        $166,564.32         $13,880.36          $21.47
         10/99           $167,795.52         $13,982.96          $21,63
       11/99-9/00        $169,745.04         $14,145.42          $21.88
         10/00           $171,036.36         $14,253.03          $22.05
       11/00-9/01        $173,081.04         $14,423.42          $22.31
         10/01           $174,402.36         $14,533.53          $22,48
       11/01-9/02        $176,494.56         $14,707.88          $22.75
         10/02           $177,845.88         $14,820.49          $22.92
       11/02-9/03        $179,985.60         $14,998.80          $23.20
    10/1/03-10/19/03                         $ 9,192.81*
</TABLE>

          * Prorated for partial month.

                               ADDITIONAL TERMS
                               ----------------

     1.   Space 2 shall be delivered on or prior to August 1, 1996 (subject to
Additional Term 2 below) "as is. "LANDLORD shall perform no demolition or base
building work for Space 2.

     2.   The date August 1, 1996 above may be executed for any period of delay
in delivery of possession of Space 2 caused by any of the causes described in
Section 27 of the Lease or failure of the present tenant of Space 2 to vacate
Space 2 prior to August 1, 1996, IN WHICH CASE THE DATES SET FORTH IN CLAUSES A,
B, C, & D HEREIN ABOVE SHALL BE DELAYED FOR A PERIOD OF TIME EQUAL TO SUCH
PERIOD OF DELAY.

     3.   LANDLORD shall provide TENANT with an allowance of $30 per rentable
square foot of Space 2 (the "Allowance") to be applied for the improvements to
be installed in Space 2 (the "TENANT'S Work"), including all required demolition
and the cost of

                                      -2-
<PAGE>

acquiring and installing telephone equipment and cabling, MEP engineering fees,
signage and security system.  No portion thereof shall be used for space
planning or for furniture or moving costs.  Such Allowance shall be disbursed in
accordance with and be subject to all the terms and conditions of Section 5 of
Appendix C to the Lease as if it were the Allowance specified therein and
TENANT's Work described in this Amendment was the TENANT's Work specified
therein.  TENANT's Work and the plans therefor shall be subject to all of the
terms of the Lease applicable to the original TENANT's Work described therein
and the plans therefor.

     4.   TENANT understands that LANDLORD will not sign this Amendment until
the present tenant of Space 2 agrees to terminate its lease as to Space 2 upon
terms and conditions satisfactory to LANDLORD.  TENANT agrees that this
Amendment is signed by TENANT and that it may be executed by LANDLORD at any
time on or prior to June 30, 1996.  TENANT agrees not to revoke its execution
hereof prior to July 1, 1996.  TENANT agrees that LANDLORD may sign this
Amendment whether or not LANDLORD signs the First Amendment.

     5.   TENANT represents that TENANT has dealt directly with and only with
Corporetum Development Company and Stein and Company Corporate Service, Inc. as
broker in connection with this Amendment and agrees to indemnify and hold
LANDLORD harmless from all claims or demands of any other broker or brokers for
any commission alleged to be due such broker or brokers as a result of any
agreement or alleged agreement with TENANT regarding this Amendment.  LANDLORD
shall indemnify and hold TENANT harmless from all claims or demands of
Corporetum Development Company and Stein and Company Corporate Service, Inc. or
any other broker alleging a commission due to such broker as a result of any
agreement with LANDLORD regarding this Amendment.  LANDLORD will pay brokerage
fees to Stein and Company Corporate Service, Inc. pursuant to a separate
agreement.

     6.   Capitalized terms used herein and not otherwise defined shall have the
meanings ascribed to them in the Lease.

     7.   Except as hereby specifically amended, the Lease remains in full force
and effect.

     8.   Redress for any claims against LANDLORD under the Lease shall only be
made against LANDLORD to the extent of LANDLORD's interest in the PROPERTY of
which the PREMISES are a part.  The obligations of LANDLORD under the Lease
shall not be personally binding on LANDLORD, nor shall any resort be had to the
private properties of

                                      -3-
<PAGE>

LANDLORD or the investment manager or to any of their respective trustees,
boards of directors or officers, as the case may be, or to the general partners
of any beneficiaries, stockholders, employees or agents thereof.

                         LISLE PROPERTY VENTURE, INC.


                         By Robert M. Chapman
                            -------------------------
                          Its      V.P.
                              -----------------------


                         PLATINUM TECHNOLOGY, INC.


                         By M. Cullinane
                            -------------------------
                          Its CHIEF FINANCIAL OFFICER
                              -----------------------

                                      -4-
<PAGE>

                                 APPENDIX "A"

                                DIAGRAM SHOWING

                                (A)
                                (B)


                           [FLOOR PLAN APPEARS HERE]


(A) BUILDING V -- FIRST FLOOR PLAN       (B) CORPORETUM OFFICE CAMPUS
    ------------------------------           ------------------------

                                              BUILDING NUMBER SIX
                                              650 WARRENVILLE ROAD
                                              LISLE, ILLINOIS

                                              FIRST FLOOR

                                              SPACE NO. 2 -- 7,758 SQUARE FEET