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] On September 4, the team added him to their active roster, replacing George Soriano.[11]