Last December at the wrap party for the second season of “Master of None,” the show’s star and co-creator, Aziz Ansari, addressed the cast and crew. But this wasn’t the typical thank-you for hard work. Using what would politely be called a “bathroom word,” he suggested they managed to ruin Season 1 by comparison. “I don’t know how we did it,” he said, “but we did it.”

Mr. Ansari was joking, to underscore how hesitant he felt about doing another run considering how good he felt about the first. Success has brought new concerns.

At 34, he is no longer the stand-up comic joking about his young pudgy cousin Harris (who plays his grown-up and quite buff cousin in the second season). Nor is he the lovably vain city employee and failed entrepreneur from the NBC sitcom “Parks and Recreation.” Through the Netflix show; his best-selling book, “Modern Romance”; and his powerful monologue on “Saturday Night Live” after the presidential inauguration, Mr. Ansari has accomplished what Chris Rock once wrote that 1970s-era Woody Allen had done: recast the idea of what a leading man should be.

And as Mr. Allen did with “Annie Hall” and “Manhattan,” Mr. Ansari has also raised expectations of the work he puts out into the world.