Exhibit 32.1

CERTIFICATIONS OF PRINCIPAL EXECUTIVE OFFICER AND PRINCIPAL

FINANCIAL OFFICER PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES‑OXLEY ACT OF 2002

In connection with this Quarterly Report on Form 10‑Q of TCR2 Therapeutics Inc. (the “Company”) for the period ended March 31, 2023 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned, hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes‑Oxley Act of 2002, that, to the best of his or her knowledge:

the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: May 11, 2023

/s/ Garry E. Menzel

Garry E. Menzel

President, Chief Executive Officer and Director (Principal Executive Officer)

/s/ Eric Sullivan

Eric Sullivan

Chief Financial Officer
(Principal Financial Officer and Principal Accounting Officer)

TCR2 THERAPEUTICS INC. 10-Q