Still, Mr. Jacobs-Jenkins finds himself in the uncomfortable position of being “a black playwright,” without knowing exactly what that means. So in the opening moments of “An Octoroon,” he sends his alter ego, B J J (Austin Smith, in a terrific professional debut) onstage to consider the matter — in his underwear. It is a fitting prologue for a play that perpetually examines itself, from every possible angle, and yet manages to transform self-consciousness from something that paralyzes into something that propels.

B J J isn’t the only undressed playwright onstage for long. He is joined by a cranky, drunken Boucicault (Haynes Thigpen), who is annoyed by how completely his star has sunk since his death some hundred years ago.

But the show must go on, and the writers, it seems, are short on actors, for reasons political as well as practical. So B J J puts on whiteface, the better to portray both the hero (the idealistic young heir to a plantation) and villain (a wicked, lust-ridden, newly rich overseer). Since Boucicault will be playing an American Indian, he slaps on redface. And his assistant (Ian Lassiter), who looks rather like a Native American, blackens up to embody both an old family retainer and an addlebrained boy slave.

From the get-go, Mr. Jacobs-Jenkins is cannily exploiting the assumption of false identity that is the starting point for theater, to make us question who is who or who is what. The detailed variations on this theme multiply into dizziness.

For instance, a white baby doll, standing in for an infant slave, is given a partly blacked-up face. And try to guess who that is dressed up as a Beatrix Potter-style rabbit. (Psst, it could well be Mr. Jacobs-Jenkins himself.)