Manske is the sixth former Iowa State player to transfer to Penn State, following fellow quarterback Rocco Becht.
Becht leaves Iowa State with 9,274 passing yards.
Burkle has one year of eligibility remaining.
Artis didn't see any action in 2025.
Neal is the third transfer to commit to Penn State.
Shanahan Jr. will follow former offensive line coach Phil Trautwein to Gainesville.