NEW YORK >> John Mulaney’s second trip to Broadway took little convincing. He didn’t even need to look at the script before signing on.

“I was like, ‘OK, well, send it to me. I’ll read it.’ And they sent it to me. I didn’t read it. I just agreed immediately,” the actor-comedian said.

What Mulaney signed up for was “All In: Comedy About Love,” a stage adaptation of his friend Simon Rich’s short stories that’s charming Broadway audiences this winter with a starry cast.

Joining Mulaney — who made his Broadway debut in 2016 with “Oh, Hello” — is Renée Elise Goldsberry, Richard Kind and Fred Armisen.

“All In” opens with the surreal story of a guy who walks into a bar that has a 12-inch piano player and then goes on to feature personal ads from dogs — “Full disclosure: I’m neutered but no complaints yet,” reads one — a love triangle involving The Elephant Man, an aging talent agent confronting Death and a history report from the 2070s.

“These are such meticulously, beautifully written pieces,” Mulaney said. “Because they so naturally lend themselves to performing, it’s very fun to take it off the page.”

Director Alex Timbers first approached Rich, the son of noted critic Frank Rich, with the idea of transferring some of his short stories to the stage.

“Our first reading was 4 ½ hours long so it took some process of elimination, but we eventually found a batch of stories that we felt were not just thematically linked, but would lend themselves to powerful performances by talented actors,” Rich said.

Once they found the right stories, attention went to presenting them: How many actors should there be? How much of a production should the 90-minute play be? Should there be costumes and sets?

They landed on minimalism and four actors, which offered both a chance to showcase each’s versatility and make the play more intimate. The show is enlivened by original illustrations from New Yorker cartoonist Emily Flake and the band The Bengsons playing love songs from The Magnetic Fields’ catalog.