UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

(Rule 14a-101)

INFORMATION REQUIRED IN PROXY STATEMENT

SCHEDULE 14A INFORMATION

Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act of 1934

(Amendment No. )

Filed by the Registrant ☐

Filed by a Party other than the Registrant ☒

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☐ Preliminary Proxy Statement

☐ Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

☐ Definitive Proxy Statement

☒ Definitive Additional Materials

☐ Soliciting Material Under § 240.14a-12

MARTIN MIDSTREAM PARTNERS L.P.

(Name of Registrant as Specified In Its Charter)

NUT TREE CAPITAL MANAGEMENT L.P.

NUT TREE CAPITAL MANAGEMENT GP, LLC

JARED R. NUSSBAUM

CASPIAN CAPITAL L.P.

CASPIAN CAPITAL GP LLC

ADAM COHEN

DAVID CORLETO

(Name of Persons(s) Filing Proxy Statement, if other than the Registrant)

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☒ No fee required

☐ Fee paid previously with preliminary materials

☐ Fee computed on table in exhibit required by Item 25(b) per Exchange Act Rules 14a-6(i)(1) and 0-11

Nut Tree Capital Management L.P., a Delaware limited partnership (“Nut Tree”), and Caspian Capital L.P., a Delaware limited partnership (“Caspian”), together with the other participants named herein, have filed a definitive proxy statement and accompanying GOLD proxy card with the Securities and Exchange Commission (“SEC”) to be used to solicit votes in connection with their opposition to proposals to be presented at a special meeting of common unitholders (the “Special Meeting”) of Martin Midstream Partners L.P., a Delaware limited partnership (the “Company”), in connection with the Company’s agreement and plan of merger with Martin Resource Management Corporation and certain of its affiliates.

On December 8, 2024, Nut Tree and Caspian issued an Investor Presentation titled “The Case for Voting AGAINST the MMLP-MRMC Merger,” a copy of which is attached hereto as Exhibit 1 and incorporated herein by reference.