Paul Nolan and Jessie Fisher will take part in the evening at the Hammerstein Ballroom.
The production has also canceled several performances to accommodate the schedule of cast member Patricia Clarkson.
The drama has recouped its investment.
The Tony-winning pop icon will perform alongside her Broadway leading man.
The fourth annual event revisits Barrington Stage this February.
The musicals will unite for the New York Cares Coat Drive.
Downton Abbey scribe Julian Fellowes will adapt the Jack Black film for the stage.