Settling into a chair at his Los Angeles headquarters for an interview that will last almost two hours, Allen turns on the TV to show off his new acquisition. He says he’s not planning to make major changes to his trophy network, but he wouldn’t mind more levity. One of the first new shows he’s approved—Storm of Suspicion, about criminals who use the weather as an ­alibi—might help. “I thought, That’s a good one,” Allen says. “ ‘Hey, I didn’t drown them. A hurricane came along!’ ” He throws his hands up and looks around the room in mock innocence.

Visiting with Allen feels like being at a private comedy show, which you’d expect given his biography. He’s spent decades working in comedy, starting in the mid-’70s at age 14 when, with his mother’s permission, he became a writer for the entertainer Jimmie Walker. He did stand-up on The Tonight Show Starring Johnny Carson in 1979, then went on to co-host NBC’s proto-reality show Real People before transforming into a talk show host ­after its run ended in 1984.