Veneziano returned to action in 2021 with the Quad Cities River Bandits, making 22 starts and logging a 6–4 record and 3.75 ERA with 127 strikeouts across 93+2⁄3 innings pitched.[5] Veneziano spent 2022 with the Double–A Northwest Arkansas Naturals, making 26 appearances (25 starts) and posting a 6–9 record and 5.72 ERA with 129 strikeouts.
Veneziano started the 2023 season with Northwest Arkansas before being promoted to the Triple–A Omaha Storm Chasers during the season.[6] In 26 games (25 starts) split between the two clubs, he registered a cumulative 10–5 record and 3.55 ERA with 127 strikeouts in 132 innings pitched. On September 19, 2023, Veneziano was selected to the 40-man roster and promoted to the major leagues for the first time.[7] He made only two appearances in his rookie season, pitching 2+1⁄3 scoreless innings.
Veneziano was optioned to Triple–A Omaha to begin the 2024 season.[8] In two games for the Royals, he compiled a 4.50 ERA with two strikeouts across two innings. Veneziano was designated for assignment by Kansas City on September 1.[9]
Miami Marlins
On September 3, 2024, Veneziano was claimed off waivers by the Miami Marlins.[10] The next day, the team added him to their active roster, replacing George Soriano.[11] Veneziano made 10 appearances down the stretch for Miami, posting a 1-0 record and 3.18 ERA with 12 strikeouts across 11+1⁄3 innings pitched.
Veneziano made 24 appearances for Miami in 2025, recording a 4.71 ERA with 20 strikeouts over 21 innings of work. He was designated for assignment by the Marlins following the promotion of Jakob Marsee on August 1, 2025.[12]
St. Louis Cardinals
On August 4, 2025, Veneziano was claimed off waivers by the St. Louis Cardinals.[13] In two appearances for the Cardinals, he recorded a 4.50 ERA with five strikeouts over four innings of work. On November 6, Veneziano was removed from the 40-man roster and sent outright to the Triple-A Memphis Redbirds, however he instead elected to become a free agent.[14]
SSG Landers
On December 15, 2025, Veneziano signed a minor league contract with the Texas Rangers.[15] He was released on January 10, 2026, in order to pursue an opportunity overseas.[16] On January 19, Veneziano signed with the SSG Landers of the KBO League, filling the spot vacated by Drew VerHagen after he failed his physical.[17]