There’s a new theater company on the South Florida scene, and if its debut production is any indication, Island City Stage will be a troupe worth watching.

Performing initially at Fort Lauderdale’s Empire Stage, Island City hopes to get its own space in Wilton Manors or Oakland Park. Artistic director Andy Rogow notes that the company wants to “…produce works that explore the values and issues that art of interest to the LGBT and progressive communities.”

The first show, Tom Jacobson’s The Twentieth-Century Way, hews to that mission in fascinating fashion.

The play is inspired by a real moment in gay history. In 1914, two out-of-work actors, B.C. Brown (Michael Westrich) and W.H. Warren (Clay Cartland), convinced the Long Beach, Calif., police department to let them conduct an operation entrapping and arresting gay men in public restrooms. The title refers to the combination of modern cleanliness, public facilities and the introduction of the zipper (vs. trouser fly buttons) – which made quick, anonymous oral sex more appealing and easier to accomplish.

Thirty-one men fell victim to the actors’ scheme, with an arrest carrying the possibility of up to 15 years in prison. Public humiliation was, at least for one man, too much to bear. So that toll included a suicide.

Jacobson could have written a realistic drama about the actors, but his approach in The Twentieth-Century Way is far more intriguing and challenging. The playwright serves up a Pirandellian exploration of the sometimes thin line between actors (or us civilians) and the roles they play. Initially presenting Brown and Warren as actors auditioning for the same movie role, Jacobson swiftly blurs the divide between performer and character, in increasingly inventive, dizzying and dangerous ways.

Each actor in the Island Stage plays numerous parts: the auditioning actors, cops, an investigative reporter and his crusty editor, a lawyer and various vividly drawn victims of Brown and Warren’s scheme. The challenge for director Michael Leeds and the two performers is to keep the story clear as the play hurtles forward, its distinctive characters appearing, vanishing and reappearing. Quite artfully, they succeed.

Cartland and Westrich employ shifting accents (you’ll hear guys from Brooklyn, Chicago, Minnesota, Scotland, Germany and more), changing costume pieces and altered physicality to portray the men perpetrating, caught up in, covering or dealing with the fallout from the entrapment scheme. Both give fearless, fine performances.

The play culminates in a full-on nude scene that, though it makes a point and ups the attentive intensity in the room, probably isn’t necessary. Still, The Twentieth-Century Way supplies plenty to ponder for Island City’s target audience and for anyone who loves theater that’s about theater.