William Luce who wrote The Belle of Amherst seems to have made a career of this kind of show. Julie Harris did one on Isak Dinesson, the title of which escapes me, and I think Mr. Luce wrote one called Lillian about Lillian Hellman.
There are two plays about Gertrude Stein and the one that starred Pat Carroll had a very satisfactory off-Broadway run. Pat Bond wrote and starred in the other which I don't think ever played NY although it was taped for PBS.
Clarence Darrow was written for Henry Fonda.
Roy Dotrice had over a decade's work as John Aubrey in the vastly entertaining Brief Lives in the 60s & 70s. He played everywhere in the English speaking world that he could get a booking.
For some reason someone thought Alec McCowan as Rudyard Kipling would sell in NYC. It didn't and died after a week. Vincent Price played Oscar Wilde and Ben Kingsley played Edmund Kean to slightly better success.
Colleen Dewhurst played Carlotta O'Neill in a show that played the Public although it went nowhere. More recently Judith Ivey played Martha Mitchell there.
There are probably quite a few more.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher