Academy Award winner Marisa Tomei, seen on Broadway in Salome and Wait Until Dark, left due to "personal family reasons."
Peet joined the previously announced Ben Stiller and Jeffrey Wright. Public producer George C. Wolfe (who is exiting the downtown Manhattan not-for-profit to be replaced by Oskar Eustis) directs the play, set for a March 11-April 10 run. Opening is March 27.
Peet is known for supporting roles in such films as "Something's Gotta Give," "The Whole Nine Yards," and "Igby Goes Down."
In This Is How It Goes, LaBute trains his eye on a small town in America for what is billed as a "new tale of manipulation, exploitation, race and infidelity," through "the story of an interracial love triangle."
Stiller is widely known for his comedic turns in such films as "Meet The Parents," "There's Something About Mary," "The Cable Guy" and "Reality Bites" — directing the latter two. The son of fellow stage veterans Jerry Stiller (Hurlyburly) and Anne Meara (Anna Christie), he has been seen on stage in the Lincoln Center Theater production of John Guare's The House of Blue Leaves, which began Off-Broadway in 1986 before transferring to Broadway.
Wright has starred on Broadway in Angels in America and Topdog/Underdog, and in Central Park in Julius Caesar. His screen credits include "Shaft" and the television movie of "Angels."
LaBute — the scribe behind bash and The Shape of Things — has enjoyed the extension of his recent Off-Broadway work, Fat Pig, and will debut a new solo work, Wrecks, at the Everyman Palace Theatre in southern Ireland's Cork this fall. He also contributed one acts to the recent inaugural Tribeca Theatre Festival and the upcoming MCC Theatre benefit.
Director Wolfe — who directed the upcoming HBO Films version of Lackawanna Blues — is also set to stage Shakepeare's A Midsummer Night's Dream this summer — his first Delacorte Theatre assignment since the 1997 mounting of the Bernstein-Comden-Green musical On the Town.
Tickets to This Is How It Goes, at The Public Theater, 425 Lafayette Street, are on sale Feb. 18. For more information, visit www.publictheater.org.