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.
Neal is the third transfer to commit to Penn State.
Shanahan Jr. will follow former offensive line coach Phil Trautwein to Gainesville.
Campbell was a key player the Nittany Lions would have loved to have back in 2026.