POWER OF ATTORNEY

        With respect to holdings of and transactions in securities issued by SQZ
Biotechnologies Company (the "Company"), the undersigned hereby constitutes and
appoints the individuals named on Schedule A attached hereto and as may be
amended from time to time, or any of them signing singly, with full power of
substitution and resubstitution, to act as the undersigned's true and lawful
attorney-in-fact to:

        1.    prepare, execute in the undersigned's name and on the
              undersigned's behalf, and submit to the United States Securities
              and Exchange Commission (the "SEC") a Form ID, including
              amendments thereto, and any other documents necessary or
              appropriate to obtain and/or regenerate codes and passwords
              enabling the undersigned to make electronic filings with the SEC
              of reports required by Section 16(a) of the Securities Exchange
              Act of 1934, as amended, or any rule or regulation of the SEC;

        2.    execute for and on behalf of the undersigned, Forms 3, 4, and 5 in
              accordance with Section 16 of the Securities Exchange Act of 1934,
              as amended, and the rules thereunder;

        3.    do and perform any and all acts for and on behalf of the
              undersigned which may be necessary or desirable to complete and
              execute any such Form 3, 4, or 5, complete and execute any
              amendment or amendments thereto, and timely file such form with
              the SEC and any stock exchange or similar authority; and

        4.    take any other action of any type whatsoever in connection with
              the foregoing which, in the opinion of such attorney-in-fact, may
              be of benefit to, in the best interest of, or legally required by,
              the undersigned, it being understood that the documents executed
              by such attorney-in-fact on behalf of the undersigned pursuant to
              this Power of Attorney shall be in such form and shall contain
              such terms and conditions as such attorney-in-fact may approve in
              such attorney-in-fact's discretion.

        The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution and resubstitution or revocation, hereby ratifying and confirming
all that such attorney-in-fact, or such attorneys-in-fact substitute or
substitutes, shall lawfully do or cause to be done by virtue of this Power of
Attorney and the rights and powers herein granted.

        The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 16th day of October, 2020.


                                        Signature:   /s/ Marc Schegerin
                                                     ------------------
                                        Print Name:  Marc Schegerin


                                      Schedule A
                                      ----------

        Individuals Appointed as Attorney-in-Fact with Full Power of
Substitution and Resubstitution

Teri Loxam
Lawrence Knopf
Alexandra Balcom