I'm not sure if there are many platformers like that. I don't even remember the existence of such a game I played.
The only closest game I remember is Sonic the Hedgehog 3. If you want you can start the game with a companion animal that is like a fox with multiple tails so it can fly like a helicopter (what a logic lol). However instead of switching character on the fly, player can control this character via 2nd gamepad to make themselves fly above places Sonic cannot reach. However existence of this fox character is not needed at all to beat the game. Why it exist and what the hell is this animal is a big mystery to me that I never bothered to learn because I was never interested in Sonic per se lol. But this character just allows a convenient way to explore places Sonic cannot reach if the player optionally wants to.