<PAGE>

                                                                   EXHIBIT 10.20

                                AMENDMENT #6 TO
                             CONSULTING AGREEMENT



     This Amendment #6 to Consulting Agreement, dated as of September 14, 2000,
hereby amends the terms of that certain Consulting Agreement dated November 17,
1995, as amended, (hereinafter "Consulting Agreement") by and between Parametric
Technology Corporation, a Massachusetts corporation, having its principal
business address at 128 Technology Drive, Waltham, Massachusetts 02453
(hereinafter "PTC") and Michael E. Porter, an individual currently residing at
44 Green Hill Road, Brookline, Massachusetts 02146 (hereinafter "Consultant").


Article 3  Services To Be Performed By Consultant, is hereby amended by adding
the following Section 3.6:

   3.6  Consultant is engaged pursuant to this Amendment #6 to Consulting
   Agreement, to participate in two (2) top management seminars, including Chief
   Information Officer (CIO) seminars, consistent with the purposes and scope
   which Consultant was previously engaged to provide under Article 3 of the
   Consulting Agreement.

Article 4 Compensation And Expenses, is hereby amended by adding the following
Section 4.7:

   4.7  Option grant for services to be performed under Section 3.6.  In
   connection with those services to be performed pursuant to this Amendment #6
   to Consulting Agreement (as described in Section 3.6 above), Consultant shall
   receive an option to purchase 20,000 shares of PTC's common stock, $.01 par
   value per share, under the terms of the Stock Option Agreement dated
   September 14, 2000 between PTC and the Consultant attached hereto.


   IN WITNESS WHEREOF, the parties have executed this Amendment #6 to Consulting
Agreement as of the date and year first above written.


Consultant                       Parametric Technology Corporation



/s/ Michael E. Porter              /s/ C. Richard Harrison
-----------------------------      ---------------------------------------
Michael E. Porter                  C. Richard Harrison
                                   President and Chief Executive Officer
<PAGE>

No. 038504                                                       20,000 Shares


                       PARAMETRIC TECHNOLOGY CORPORATION
                       1997 Incentive Stock Option Plan

                     Nonstatutory Stock Option Certificate

                              September 14, 2000

     Parametric Technology Corporation (the "Company"), a Massachusetts
corporation, hereby grants to the person named below an option to purchase
shares of Common Stock, $0.01 par value, of the Company (the "Option") under and
subject to the Company's 1997 Incentive Stock Option Plan (the "Plan")
exercisable on the following terms and conditions set forth below and those
attached hereto and in the Plan:

Name of Optionholder:             Michael E. Porter

Social Security Number            ###-##-####

Number of Shares:                 20,000

Option Price:                     $ 13.1875

Date of Grant:                    September 14, 2000

Expiration:                       September 14, 2005

Exercisability Schedule:

        on or after September 14, 2000, as to 50% of the shares,
        on or after October 1, 2000, as to 50% of the shares,

   provided that Optionholder's consulting agreement with the Company is not
   terminated earlier, in which event the Option, (i) to the extent exercisable
   at the date of such termination, may not be exercised as to any shares after
   the expiration of seven (7) months from the date of such termination, and
   (ii) to the extent not exercisable at the date of such termination, shall be
   canceled as to any such shares effective on the date of such termination.

     This Option shall not be treated as an Incentive Stock Option under section
422 of the Internal Revenue Code of 1986, as amended.

     By acceptance of this Option, the Optionholder agrees to the terms and
conditions set forth above and those attached hereto and in the Plan.


OPTIONHOLDER                       PARAMETRIC TECHNOLOGY CORPORATION



By: /s/ Michael E. Porter          By: /s/ Edwin J. Gillis
    ---------------------------    -----------------------------------
    Optionholder                   Executive Vice President - CFO
<PAGE>

       PARAMETRIC TECHNOLOGY CORPORATION 1997 INCENTIVE STOCK OPTION PLAN

                 Nonstatutory Stock Option Terms And Conditions


     1.   Plan Incorporated by Reference.  This Option is issued pursuant to the
          ------------------------------
terms of the Plan and may be amended as provided in the Plan. Capitalized terms
used and not otherwise defined in this certificate have the meanings given to
them in the Plan.  This certificate does not set forth all of the terms and
conditions of the Plan, which are incorporated herein by reference.  The
Committee administers the Plan and its determinations regarding the operation of
the Plan are final and binding.  Copies of the Plan may be obtained upon written
request without charge from the Corporate Counsel of the Company.

     2.   Option Price.  The price to be paid for each share of Common Stock
          ------------
issued upon exercise of the whole or any part of this Option is the Option Price
set forth on the face of this certificate.

     3.   Exercisability Schedule.  This Option may be exercised at any time and
          -----------------------
from time to time for the number of shares and in accordance with the
exercisability schedule set forth on the face of this certificate, but only for
the purchase of whole shares.  This Option may not be exercised as to any shares
after the Expiration Date.

     4.   Method of Exercise.  To exercise this Option, the Optionholder shall
          ------------------
deliver written notice of exercise to the Company specifying the number of
shares with respect to which the Option is being exercised accompanied by
payment of the Option Price for such shares in cash, by certified check or in
such other form, including shares of Common Stock of the Company valued at their
Fair Market Value on the date of delivery or a payment commitment of a financial
or brokerage institution, as the Committee may approve. Promptly following such
notice, the Company will deliver to the Optionholder a certificate representing
the number of shares with respect to which the Option is being exercised.

     5.   No Right To Employment. No person shall have any claim or right to be
          ----------------------
granted an Option.  Each employee of the Company or any of its Affiliates is an
employee-at-will (that is to say that either the Participant or the Company or
any Affiliate may terminate the employment relationship at any time for any
reason or no reason at all) unless, and only to the extent, provided in a
written employment agreement for a specified term executed by the chief
executive officer of the Company or his duly authorized designee or the
authorized signatory of any Affiliate.  Neither the adoption, maintenance, nor
operation of the Plan nor any Option hereunder shall confer upon any employee of
the Company or of any Affiliate any right with respect to the continuance of
his/her employment by the Company or any such Affiliate nor shall they interfere
with the right of the Company (or Affiliate) to terminate any employee at any
time or otherwise change the terms of employment, including, without limitation,
the right to promote, demote or otherwise re-assign any employee from one
position to another within the Company or any Affiliate.

     6.   Effect of Grant.  Participant shall not earn any Options granted
          ----------------
hereunder until such time as all the conditions put forth herein and in the Plan
which are required to be met in order to exercise the Option have been fully
satisfied.

     7.   Recapitalization, Mergers, Etc.  As provided in the Plan, in the
          ------------------------------
event of corporate transactions affecting the Company's outstanding Common
Stock, the number and kind of shares subject to this Option and the exercise
price hereunder shall be equitably adjusted. If such transaction involves a
consolidation or merger of the Company with another entity, the sale or exchange
of all or substantially all of the assets of the Company or a reorganization or
liquidation of the Company, then in lieu of the foregoing, the Committee may
upon written notice to the Optionholder provide that this Option shall terminate
on a date not less than 20 days after the date of such notice unless theretofore
exercised. In connection with such notice, the Committee may in its discretion
accelerate or waive any deferred exercise period.

     8.   Option Not Transferable.  This Option is not transferable by the
          -----------------------
Optionholder otherwise than by will or the laws of descent and distribution, and
is exercisable, during the Optionholder's lifetime, only by the Optionholder.
The naming of a Designated Beneficiary does not constitute a transfer.
<PAGE>

     9.   Termination of Employment or Engagement.  If the Optionholder's status
          ----------------------------------------
as an employee or consultant of (a) the Company, (b) an Affiliate, or (c) a
corporation (or parent or subsidiary corporation of such corporation) issuing or
assuming a stock option in a transaction to which section 424(a) of the Code
applies, is terminated for any reason (voluntary or involuntary) and the period
of exercisability for a particular Option following such termination has not
been specified by the Board, each such Option then held by that Participant
shall expire to the extent not previously exercised ten (10) calendar days after
such Participant's employment or engagement is terminated, except that -
                                                           ------ ----

  (a)     If the Participant is on military, sick leave or other bona fide leave
                                                                 ---- ----
of absence (such as temporary employment by the federal government), his or her
employment or engagement with the Company will be treated as continuing intact
if the period of such leave does not exceed ninety (90) days, or, if longer, so
long as the Participant's right to reemployment or the survival of his or her
service arrangement with the Company is guaranteed either by statute or by
contract; otherwise, the Participant's employment or engagement will be deemed
to have terminated on the 91st day of such leave.

  (b)     If the Participant's employment is terminated by reason of his or her
retirement from the Company at normal retirement age, each Option then held by
the Participant, to the extent exercisable at retirement, may be exercised by
the Participant at any time within three (3) months after such retirement unless
terminated earlier by its terms.

  (c)     If the Participant's employment or engagement is terminated by reason
of his or her death, each Option then held by the Participant, to the extent
exercisable at the date of death, may be exercised at any time within one year
after that date (unless terminated earlier by its terms) by the person(s) to
whom the Participant's option rights pass by will or by the applicable laws of
descent and distribution.

  (d)     If the Participant's employment or engagement is terminated by reason
of his or her becoming permanently and totally disabled, each Option then held
by the Participant, to the extent exercisable upon the occurrence of permanent
and total disability, may be exercised by the Participant at any time within one
(1) year after such occurrence unless terminated earlier by its terms. For
purposes hereof, an individual shall be deemed to be "permanently and totally
disabled" if he or she is unable to engage in any substantial gainful activity
by reason of any medically determinable physical or mental impairment which can
be expected to result in death or which has lasted or can be expected to last
for a continuous period of not less than twelve (12) months. Any determination
of permanent and total disability shall be made in good faith by the Company on
the basis of a report signed by a qualified physician.

     10.  Compliance with Securities Laws.  It shall be a condition to the
          -------------------------------
Optionholder's right to purchase shares of Common Stock hereunder that the
Company may, in its discretion, require (a) that the shares of Common Stock
reserved for issuance upon the exercise of this Option shall have been duly
listed, upon official notice of issuance, upon any national securities exchange
or automated quotation system on which the Company's Common Stock may then be
listed or quoted, (b) that either (i) a registration statement under the
Securities Act of 1933 with respect to the shares shall be in effect, or (ii) in
the opinion of counsel for the Company, the proposed purchase shall be exempt
from registration under that Act and the Optionholder shall have made such
undertakings and agreements with the Company as the Company may reasonably
require, and (c) that such other steps, if any, as counsel for the Company shall
consider necessary to comply with any law applicable to the issue of such shares
by the Company shall have been taken by the Company or the Optionholder, or
both.  The certificates representing the shares purchased under this Option may
contain such legends as counsel for the Company shall consider necessary to
comply with any applicable law.

     11.  Payment of Taxes.  The Optionholder shall pay to the Company, or make
          ----------------
provision satisfactory to the Company for payment of, any taxes required by law
to be withheld with respect to the exercise of this Option.  The Committee may,
in its discretion, require any other Federal or state taxes imposed on the sale
of the shares to be paid by the Optionholder. In the Committee's discretion,
such tax obligations may be paid in whole or in part in shares of Common Stock,
including shares retained from the exercise of this Option, valued at their Fair
Market Value on the date of delivery.  The Company and its Affiliates may, to
the extent permitted by law, deduct any such tax obligations from any payment of
any kind otherwise due to the Optionholder.


     Adopted November 14, 1996