The "plomedy" follows four Italian-Americans who take their issues into their own hands.
Alfonso will star alongside James Earl Jones, Rose Byrne, and Annaleigh Ashford.
James Wirt costars in Scott Organ's dark romantic comedy.
According to rumors, the show would hit New York in the 2015-16 season.
The reading of the new play by Matthew-Lee Erlbach is directed by Wes Grantom.
Full casting for the production has been announced.
The company will also present a musicalized version of Truman Capote's short story "A Christmas Memory."
Joe Iconis will host the event and perform a 30-minute set at 54 Below.
Richard Chamberlain, Holly Hunter, Bill Pullman, and more star in the play.
54 Below will host this special one-night concert featuring the film's cast.