Ann Washburn showed us in Woolly Mammoth Theatre’s divine, “Simpsons”-inspired “Mr. Burns, a Post-Electric Play” that the Homer whom playwrights turn to for inspiration doesn’t have to have come from a time before Christ. TV, in fact, may well be on its way to challenging the Greeks as a primary source for writers with offbeat dramatic intentions.

Witness, for example, the latest off-Broadway effort from David Adjmi, whose seriocomedy about cosseted Brooklyn wives, “Stunning,” had an auspicious premiere at Woolly in 2008. Like Washburn’s “Mr. Burns,” Adjmi’s new work, the fascinating “3C,” explores heretofore uncharted resonances in characters from the annals of TV — who historically had no more depth than the figures you find in coloring books.

Anna Chlumsky, Kate Buddeke, Hannah Cabell and Jake Silbermann in a scene from David Adjmi’s play, “3C”, performing off-Broadway at Rattlestick Playwrights Theater in New York. (Joan Marcus/AP)

His source material for the 90-minute piece at Greenwich Village’s Rattlestick Theater comes from — are you ready? — “Three’s Company,” a sitcom relic of the singles-swinging ’70s featuring John Ritter, Suzanne Somers and Joyce DeWitt as roommates sharing a Santa Monica apartment. While the play is in need of dramaturgical triage — its attempts at once to satirize and deepen the show’s format on a stage fall out of balance — Adjmi’s experiment is fun to watch and ponder. In repurposing “Three’s Company” as a tragicomedy, he is seeking to invent a whole new sub-genre: the sitcom, if you will, of pain.

Director Jackson Gay’s uneven production offers up a cast with some members more accomplished than others. Best are Anna Chlumsky (most recently seen on HBO’s “Veep” ) as an almost anesthetized inheritor of Somers’s Chrissy Snow shtick, and Kate Buddeke, portraying an amusingly shorter-fused version of the landlady, Mrs. Roper, played on the long-running series by Audra Linley. They along with Eddie Cahill, in a turn as a skeevy skirt-chasing neighbor, are most successful at conveying both the vapid veneer of a stock TV character, and the essence of a human being with the sort of complex agenda that television comedy of the time could not possibly have accommodated.

What evolves over an hour and a half in Apartment 3C is the simultaneous exposition of goofy exploits — courtesy of the character modeled on Ritter’s Jack Tripper and played by Jake Silbermann — and uncovering of the characters’ devastating secrets. Like Jack, for instance, Silbermann’s Brad appears to be gay — to the landlords, an acceptably non-threatening tenant in an apartment with women. Adjmi, though, adds suffering to the character’s emotional resume: He really is tormented by his sexuality. This turns out to be a version of “Three’s Company” that has more in common with Ibsen than Wilde.

Aligning the arcs of situation comedy and tragedy is a tall order, one that isn’t always successfully filled here. But in creating awkward silences where a laugh track might be, Adjmi is headed in a compelling direction.

“3C,” at the Rattlestick Playwrights Theater through July 14. Tickets: $55.