Maybe if they could get in-orbit refueling to work on the Falcon? IIRC, Starship would require that for trips out of LEO, anyway. Nobody has done it before with a crewed rocket, and there's been some criticism that Starship's plan relies on this thing that hasn't been proven.

The Lunar Gateway is supposed to have a final assembled mass of 63 metric tons. May or may not be able to make that work at all with Falcon.