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SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE TO

TENDER OFFER STATEMENT

Under Section 14(d)(1) or 13(e)(1)

of the Securities Exchange Act of 1934

(Amendment No. 1)

BlackRock MuniVest Fund, Inc.

(Name of Subject Company (Issuer))

BlackRock MuniVest Fund, Inc.

(Names of Filing Person(s) (Issuer))

Shares of Common Stock, Par Value $0.10 per share

(Title of Class of Securities)

09253R105

(CUSIP Number of Class of Securities)

John M. Perlowski

BlackRock MuniVest Fund, Inc.

50 Hudson Yards

New York, New York 10001

(800) 882-0052

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications on Behalf of Filing Person(s))

Copies to:

July 15, 2025

(Date Tender Offer First Published, Sent or Given to Security Holders)

Check the appropriate boxes below to designate any transactions to which this statement relates:

Check the following box if the filing is a final amendment reporting the results of the tender offer. ☐

This Amendment No. 1 (“Amendment No. 1”) amends and supplements the Issuer Tender Offer Statement on Schedule TO filed on July 15, 2025 (the “Schedule TO”) by BlackRock MuniVest Fund, Inc., a Maryland corporation (the “Fund”), pursuant to Rule 13e-4 under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), in connection with an offer by the Fund (the “Offer”) to repurchase 2.5% of its issued and outstanding shares of common stock, par value $0.10 per share (the “Shares”), in exchange for cash at a price equal to 98% of the net asset value (“NAV”) per Share determined as of the close of the regular trading session of the New York Stock Exchange, the principal market on which the Shares are traded, on the next day the NAV is calculated after the Offer expires, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated July 15, 2025 (the “Offer to Purchase”), and in the related Letter of Transmittal, copies of which were previously filed as Exhibits (a)(1)(i) and (a)(1)(ii), respectively, to the Schedule TO.

This Amendment No. 1 is being filed to update Item 12 of the Schedule TO to include a press release announcing the preliminary results of the Offer, which expired on August 15, 2025, at 5:00 p.m. Eastern time. A copy of the press release is attached hereto as Exhibit (a)(5)(ii).

Except as specifically provided herein, the information contained in the Schedule TO, as amended, and the Letter of Transmittal remains unchanged, and this Amendment No. 1 does not modify any of the information previously reported in the Schedule TO, as amended, or the Letter of Transmittal.

Item 1 through Item 9 and Item 11

The information set forth in the Offer to Purchase and the related Letter of Transmittal is incorporated by reference into this Amendment No. 1 in answer to Item 1 through Item 9 and Item 11 of the Schedule TO.

(a) The audited annual financial statements of the Fund dated July 31, 2024 and the schedule of investments of the Fund dated July 31, 2024, both filed with the SEC on EDGAR on Form N-CSR on October 3, 2024, are incorporated by reference. The unaudited semi-annual financial statements of the Fund dated January  31, 2025 and the schedule of investments of the Fund dated January 31, 2025, both filed with the SEC on EDGAR on Form N-CSRS on April 7, 2025, are incorporated by reference.

(b) Not applicable.

Item 12(a) of the Schedule TO is hereby amended and supplemented to add the following exhibit:

(a)(5)(ii) Press release issued on August 18, 2025 is filed herewith.

Filing Fee Exhibit is filed herewith.

Not applicable.

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SIGNATURE

After due inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

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Exhibit Index

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