“NOËL COWARD’S FANTASTIC, but all I could think was: What’s the use of having an American one?” Greenberg says to me one afternoon in December from across a vinyl booth at Chelsea’s Rail Line Diner, the playwright’s de facto office. In person, his round face and pale, swooping crest of hair suggest a kind of aged version of Philip Seymour Hoffman, especially Hoffman as Truman Capote, whom the actor played in the 2005 biopic. Greenberg adapted Capote’s 1958 novella, “Breakfast at Tiffany’s,” into a Broadway play in 2013, but the similarities between the two gay men have less to do with their characters’ lyricism and their glamorous-but-intellectual mise-en-scène — one full of massive Manhattan homes and the rich people who inhabit them — than the way Greenberg goes about his life: The only guests allowed in his duplex apartment, where he’s lived alone, across the street from the diner, for 15 years, seem to be the few close female friends for whom he enjoys cooking elaborate dinners. Chief among them is the actress Patricia Clarkson — one of Greenberg’s “swans,” as Clarkson has referred to these women — who graduated from Yale’s School of Drama with him in the ’80s and has remained in communication ever since, occasionally interrupting our diner conversation by texting photographs of her niece’s toddler.

“I don’t know why America would have a Noël Coward — it just seems culturally inappropriate,” Greenberg continues after cooing over the child on his phone screen. “And then you think, ‘Well, how can I be less like that today?’” Not unlike one of his characters, he’s now midway through a long monologue about something someone said about his aesthetic decades ago, but the point lingers long after he’s caught his breath: Greenberg isn’t interested in his work sounding or feeling like any of his forebears, legendary as they may be. Nor is he invested in chasing trends: not structural trickery, or set-driven surprise, or audience participation or any other innovations currently informing the theater; instead, he remains a realist, a classicist driven by story above all, mostly because, he says, “It’s possible to be stunningly derivative trying to do something other people are doing.” And despite being one of America’s most established playwrights, having had around 30 shows either on or off Broadway staged in the past four decades, he’s also not really concerned with repeating any of his trademark flourishes. “What I don’t see is someone relying on what’s worked in the past,” says the actress Maddie Corman, who in 2016 appeared in Greenberg’s “The Babylon Line” at Lincoln Center Theater. “Richard is someone whose work is always pushing forward, which is rare. Once you’ve become successful at something, people have expectations — and I don’t think he cares about that.”

Indeed, in an era when some playwrights have become as famous as the actors in their casts, when the experience of going to the theater, the whole Instagram-the-Playbill moment of it all, is often just as motivating to ticket buyers as the play itself, Greenberg remains one of the few dramatists who’s remained relevant simply for what he’s put on the page. Though he’s workshopped new pieces often, several directors and actors told me that he doesn’t meddle too much in the casting or the staging; in fact, he goes to rehearsals only begrudgingly. Instead, he sends copious notes, and his scripts’ stage directions communicate his intentions. These parentheticals are typically among his most evocative lines; a memorable example from “Take Me Out” goes: “Anyway, those Greeks … they … (i.e.: were big faggots). And they created … (He makes a big circular gesture with his arms to indicate ‘civilization and stuff’).” Greenberg also has never written for streaming television, which, crowded with well-spoken, almost implausibly quick-witted characters, is undoubtedly indebted to his plays, whether it’s HBO’s “Succession” or Apple’s “The Morning Show.” And given his decades of output, relatively few of his plays have seen a revival, partly because he feels that certain lines reek too embarrassingly of youth.

In that sense, even the political undertones of “Take Me Out” now feel archaic, which is why the only change he insisted upon was that the production take place not in the present, which is how it was originally written, but sometime in the mid-90s, when Greenberg was actually conceiving the play. “Before this came together, I was looking forward to that democracy monologue as something that marked how different things were between that time and now. But it’s just incomprehensible: forces — anger, for instance — exist now that didn’t exist then,” he says. “I like things that alert us to how different the past was as opposed to how similar.”