Not just a supporting character that steals the show in one movie, but one that actually ends up taking over the franchise itself.

I was watching Tremors: Shrieker Island a few days ago and the question came to mind.

Michael Gross’ Burt Gummer pretty much did it all in that franchise.
He went from supporting character (and comedy relief) in the original, to co-Star in the sequel, to Starring in the third, to leading a TV show based on the movie to playing his own grandfather in the fourth movie. Movies five through seven saw him fight Graboids in extremely different terrains, while in universe he became something of a legend in certain circles after 30 years of cryptid combat.

So yeah, looking for other examples of that type.