The curtain rises, but the actors onstage don’t know how the show begins. Nor do they know what the story is, which actor plays what role, or who those characters are, exactly. This is not a description of an actor’s nightmare, but of a very real, entirely improvised play, called “Stolen House,” that takes place on borrowed stage sets.

When it arrives for late-night performances in Manhattan this weekend, the cast members will make themselves at home on sets used for current productions at the Anne L. Bernstein Theater (the Victorian drawing room of “Perfect Crime”) and the Barrow Street Theater (the clinical environment of “The Effect”). From there, an unscripted two-act play will unfold.

It helps that the cast is made up of a supergroup of improv stars: the Chicago duo TJ Jagodowski and David Pasquesi (better known as TJ and Dave); the members of the Los Angeles team WeirDass, Stephnie Weir and Bob Dassie; and the New Yorkers Scott Adsit and John Lutz. All six are comedians with credits like “30 Rock” (Mr. Adsit and Mr. Lutz), “MadTV” (Ms. Weir) and “Veep” (Mr. Pasquesi), and each excels at the kind of long-form improv popularized in New York by the Upright Citizens Brigade. But the “Stolen House” crew specializes in a slower, more patient version grounded in everyday relationships.

The show is the brainchild of the stars, as well as of the director Stephen Ruddy and the Barrow Street Theater producer Scott Morfee. Mr. Ruddy has long sought to find overlap between scripted theater and spontaneous performance. He has produced “Gravid Water,” a show that matches improvisers with actors who have memorized lines from scripts, playing at the UCB Theater since 2004. When he saw the Broadway production of “August: Osage County” in 2008, Mr. Ruddy imagined what skilled improvisers could do on its elaborate, multilevel set. Years later, he proposed the “Stolen House” concept to the best and most theatrical improvisers he could think of — who all had worked in “Gravid Water.”