Presidio Production Co-A美股招股说明书(2026-05-14版)

PRESIDIO PRODUCTION COMPANY 11,887,469 SHARES OF CLASS A COMMON STOCK ISSUABLEUPON THE EXERCISE OF WARRANTS 133,332 WARRANTS 29,757,255 SHARES OF CLASS A COMMON STOCK This Prospectus Supplement updates and supplements theprospectus dated March 23, 2026 (the “Prospectus”), which forms apart of our registration statement on Form S-1 (No. 333-294316). This prospectus supplement is being filed to update and supplementthe information in the Prospectus with the information contained in our Current Report on Form 8-K, filed with the Securities andExchange Commission on May 14, 2026 (the “Current Report”). Accordingly, we have attached the Current Report to this ProspectusSupplement. The Prospectus and this Prospectus Supplement relates to the issuance by Presidio Production Company (“Presidio” or the“Company”) of up to 11,887,469 shares of Class A Common Stock, par value $0.0001 (the “Presidio Class A Common Stock”) thatmay be issued upon the exercise of the Presidio Warrants (as defined below) and the offer and sale from time to time by the sellingsecurityholders named in the Prospectus and this Prospectus Supplement (the “Selling Securityholders”), or their permitted transferees,of up to 29,757,255 shares of Presidio Class A Common Stock and up to 133,332 Presidio Warrants. The 11,887,469 shares of Presidio Class A Common Stock that may be issued upon the exercise of the Presidio Warrants that theProspectus and this Prospectus Supplement relates to include: (i) up to 11,666,637 shares of Presidio Class A Common Stock that maybe issued upon the exercise of 11,666,637 warrants to purchase Presidio Class A Common Stock at an exercise price of $11.50 pershare (the “Public Warrants”) and (ii) up to 220,832 shares of Presidio Class A Common Stock that may be issued upon the exercise of220,832 warrants to purchase Presidio Class A Common Stock at an exercise price of $11.50 per share (the “Private PlacementWarrants” and together with the Public Warrants, the “Presidio Warrants”). The shares of Presidio Class A Common Stock and Presidio Warrants offered for resale under the Prospectus and this ProspectusSupplement were issued to the Selling Securityholders (as applicable to each) in accordance with the terms of, and transactionscontemplated by, the Business Combination Agreement, dated as of August5, 2025 (the “Business Combination Agreement”), by andamong Presidio MidCo Inc., a Delaware corporation (formerly EQV Ventures Acquisition Corp., a Cayman Islands exemptedcompany) (“EQV”), Presidio (f/k/a Presidio PubCo Inc.), Prometheus PubCo Merger Sub Inc., a Delaware corporation and a direct,wholly owned subsidiary of Presidio (“EQV Merger Sub”), Prometheus Holdings LLC, a Delaware limited liability company and adirect, wholly owned subsidiary of EQV (“Prometheus Holdings”), Prometheus Merger Sub LLC, a Delaware limited liabilitycompany and a direct, wholly owned subsidiary of Prometheus Holdings (“Presidio Merger Sub”) and Presidio Investment HoldingsLLC, a Delaware limited liability company (“PIH”). The Presidio Class A Common Stock registered hereunder represents thesecurities issued to the Selling Securityholders pursuant to the terms of the Business Combination Agreement, as applicable to eachSelling Securityholder, concurrently with the closing of the transactions contemplated by the Business Combination Agreement (the“Business Combination”). The Business Combination is described in greater detail in the Prospectus. See“Prospectus Summary — The BusinessCombination.” The 29,757,255 maximum number of shares of Presidio Class A Common Stock offered for resale under the Prospectus and thisProspectus Supplement consists of: (a) 7,686,960 shares of Presidio Class A Common Stock that were issued to EQV VenturesSponsor LLC, a Delaware limited liability company, and its affiliates (the “Sponsor”) upon the conversion of 282,314 EQV Class AShares and 7,404,646 EQV Class B Shares, (b) 160,000 shares of Presidio Class A Common Stock that were issued to the formerindependent directors of EQV, upon the conversion of 160,000 EQV Class A Shares, (c) 120,000 shares of Presidio Class A CommonStock that were issued to the former independent directors of EQV, upon the conversion of 120,000 EQV Class A Shares, (d)9,315,217 shares of Presidio Class A Common Stock that were issued in connection with the PIPE Financing (as defined in theProspectus), (e) 2,717,300 shares of Presidio Class A Common Stock that may be issued upon the conversion of the 27,173 shares ofSeries B Preferred Stock, (f) 937,500 shares of Presidio Class A Common Stock that may be issued upon the exercise of warrants topurchase Presidio Class A Common Stock at an exercise price of $0.01 per share and (g) 8,806,946 shares of Presidio Class ACommon Stock issued, or that may be issued upon the conversion of Prometheus Holdings Common Units (as defined in theProspectus), to certain of the other Selling Securityholders named herein in connection with the Business Com