Allgeyer attended St. John Vianney High School in Missouri where he played baseball and ice hockey. In 2014, he was named the Metro Catholic co-player of the year.[1] As a hockey player, he led his team in goals as a senior.[2]
Allgeyer was drafted out of Iowa by the Toronto Blue Jays in the 12th round of the 2018 Major League Baseball draft, receiving a signing bonus of $125,000.[5] He was assigned to the Low-AVancouver Canadians, where he spent the remainder of the season and posted a 2.73 earned run average (ERA) in 15 games. In 2019, Allgeyer played for the High-ADunedin Blue Jays, pitching to a 3.95 ERA over 23 games and totaling 1181⁄3 innings.[6] He was named a Florida State League mid-season all-star as well as a MiLB.com organization all star for the 2019 campaign.[7] Allgeyer did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[8]
On May 15, 2021, Allgeyer was selected to the 40-man roster and promoted to the major leagues for the first time.[9] He was optioned down to Triple-A on May 17 without making an appearance.[10] On July 2, Allgeyer was recalled to the active roster and made his major league debut with a perfect ninth inning against the Tampa Bay Rays.[11] Allgeyer was designated for assignment by Toronto on July 18.[12] Allgeyer was sent outright to the Triple-A Buffalo Bisons on July 27.[13] He finished the year with a 5.34 ERA and 5–5 record across 22 appearances for Buffalo.
Allgeyer spent the entire 2022 season with Buffalo, pitching in 35 games (and starting 15) and posting a 6–6 record and 5.44 ERA with 95 strikeouts in 101.0 innings pitched.
Philadelphia Phillies
On March 25, 2023, Allgeyer was traded to the Philadelphia Phillies and assigned to the Triple-A Lehigh Valley IronPigs.[14] He made 4 starts for Lehigh Valley, recording a 4.50 ERA with 15 strikeouts in 12.0 innings pitched.
Houston Astros
On May 5, 2023, Allgeyer was traded to the Houston Astros in exchange for cash considerations.[15] In 19 games for the Triple–A Sugar Land Space Cowboys, he worked to a 5–4 record and 6.62 ERA with 70 strikeouts in 69+1⁄3 innings pitched. On August 28, Allgeyer was released by the Astros organization.[16]