Tcr2 Therapeutics (TCRR) 8-K TCR 2 Therapeutics Announces Proposed Public Offering of Common Stock

Exhibit 5.1

Goodwin Procter LLP 100 Northern Avenue Boston, MA 02210   goodwinlaw.com +1 617 570 1000

July 31, 2020

TCR² Therapeutics Inc.

100 Binney Street, Suite 710

Cambridge, MA 02142

Re:    Securities Being Registered under Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-3 (File No. 333-236965) (as amended or supplemented, the “Registration Statement”) filed on March 6, 2020 with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the offer by TCR² Therapeutics Inc. Corporation, a Delaware corporation (the “Company”) of up to $300,000,000 of any combination of securities of the types specified therein. The Registration Statement was declared effective by the Commission on April 28, 2020. Reference is made to our opinion letter dated March 6, 2020 and included as Exhibit 5.1 to the Registration Statement. We are delivering this supplemental opinion letter in connection with the prospectus supplement (the “Prospectus Supplement”) filed on July 29, 2020 by the Company with the Commission pursuant to Rule 424 under the Securities Act. The Prospectus Supplement relates to the offering by the Company of up to 9,200,000 shares of the Company’s Common Stock, par value $0.0001 per share (the “Shares”) covered by the Registration Statement. The Shares include an option granted to the underwriters of the offering to purchase 1,200,000 Shares. The Shares are being sold to the several underwriters named in, and pursuant to, an underwriting agreement among the Company and such underwriters (the “Underwriting Agreement”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinions set forth below are limited to the Delaware General Corporation Law.

TCR² Therapeutics Inc.

July 31, 2020

Page 2

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and, upon issuance and delivery against payment therefor in accordance with the terms of the Underwriting Agreement, the Shares will be validly issued, fully paid and non-assessable.

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to a current report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement and to the references to our firm under the caption “Legal Matters” in the Registration Statement and the Prospectus Supplement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ Goodwin Procter

GOODWIN PROCTER LLP