ROPES & GRAY LLP PRUDENTIAL TOWER 800 BOYLSTON STREET BOSTON, MA 02199-3600 WWW.ROPESGRAY.COM Exhibit (11)

March 5, 2021

State Street Institutional Investment Trust

1 Iron Street

Boston, Massachusetts 02210

Re: State Street U.S. Core Equity Fund and State Street Income Fund (the “Funds”)

Ladies and Gentlemen:

We are furnishing this opinion in connection with the Registration Statement on Form N-14 (the “Registration Statement”) filed under the Securities Act of 1933, as amended, by State Street Institutional Investment Trust (the “Trust”), relating to shares of the Funds (the “Shares”) to be issued in connection with the reorganization of the General Electric RSP Income Fund and the General Electric RSP U.S. Equity Fund with and into State Street Income Fund and State Street U.S. Core Equity Fund, respectively (the “Reorganizations”).

We have acted as counsel for the Trust in connection with the Reorganizations. We are familiar with the action taken by its Trustees to authorize this issuance of the Shares. We have examined its records of Trustee actions, its Amended and Restated Bylaws, and its Amended and Restated Agreement and Declaration of Trust (the “Declaration of Trust”) on file at the office of the Secretary of The Commonwealth of Massachusetts. We have examined copies of the Registration Statement, in the form filed with the Securities and Exchange Commission, and such other documents as we deem necessary for the purpose of this opinion. This opinion is given with respect to Massachusetts law, which governs the organization of, and issuance of shares by, the Trust.

We assume that upon sale of the Shares the Trust will receive the net asset value thereof.

We are of the opinion that the Trust is authorized to issue an unlimited number of Shares of each Fund; and that when the Shares are issued and sold in accordance with the Registration Statement, they will be validly issued, fully paid and, except as described in the following paragraph, nonassessable by the Trust.

The Trust is an entity of the type commonly known as a “Massachusetts business trust.” Under Massachusetts law, shareholders could, under certain circumstances, be held personally liable for the obligations of the Trust. However, the Declaration of Trust provides that shareholders shall not be subject to any personal liability for the acts or obligations of the Trust, and also requires

that every note, bond, contract, instrument, certificate or undertaking made or issued on behalf of the Trust by the trustees or any trustee, by any officer or officers or otherwise shall give notice to the effect that the obligations of such instrument are not binding on shareholders. The Declaration of Trust provides that in case any shareholder or former shareholder shall be held to be personally liable solely by reason of his or her being or having been a shareholder of the Trust or of a particular series and not because of his or her acts or omissions or for some other reason, the shareholder or former shareholder (or his or her heirs, executors, administrators or other legal representatives or, in the case of a corporation or other entity, its corporate or other general successor) shall be entitled out of the assets of the series of which he or she is a shareholder or former shareholder to be held harmless from and indemnified against all loss and expense arising from such liability. Thus, the risk of a shareholder of a series of the Trust incurring financial loss on account of such shareholder liability should be limited to circumstances in which the series itself would be unable to meet its obligations.

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Very truly yours,

/s/ Ropes & Gray LLP                

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