Power of Attorney

Know all by these presents, that the undersigned hereby constitutes
and appoints each of Margaret Siegel and Stephen Turkowiak, signing singly,
and with full power of substitution, as the undersigned's true and lawful
attorney-in-fact to:

(1) execute for and on behalf of the undersigned, in the undersigned's capacity
as an officer and/or director of TCR2 Therapeutics Inc., a Delaware corporation
(the "Company"), from time to time the following Securities and Exchange
Commission (the "SEC") forms: Forms 3, 4, and 5 in accordance with Section 16(a)

of the Securities Exchange Act of 1934, as amended (the "Exchange Act"), and
the rules thereunder;

(2) 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

(3) 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 or revocation, hereby ratifying and confirming all that
such attorney-in-fact, or such attorney-in-fact's 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, is not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Exchange Act.

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. This Power of Attorney shall expire as to any
individual attorney-in-fact if such attorney-in-fact ceases to be an officer
of the Company. This Power of Attorney may be filed with the SEC as a
confirming statement of the authority granted herein.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 4th day of May, 2020.


/s/ Stephen Webster
Printed Name: Stephen Webster