A revival would mark the musical's first time on Broadway since the short-lived 1997 premiere.
Curtis Holbrook will take Rapp's place opposite Idina Menzel while the former Rent star recovers from surgery.
Naomi Wallace presents the US premiere of her play about imprisoned teens.
Original Pippin John Rubinstein extends his run with the Broadway revival.
Previously announced cast members also include Annaleigh Ashford, Rose Byrne, Kristine Nielsen, and more.
An LCT3 production of Nick Jones' Verité has also been announced.
O'Hara will head to Williamstown while Pinkham takes the stage at Joe's Pub.
The monologist will perform his new work at California Shakespeare Theater.
The production will have played 145 performances.
Robert Schenkkan will debut part two of his LBJ cycle.