We switch flavors everyday when feeding Belle. In fact, we rotate between wet food and raw with each meal without issues, but that’s something we’ve done since she came to us as a half grown stray. We rotate flavors to keep her from getting bored with her food- chicken, rabbit, beef, duck etc.
Remember, every cat is an individual. What works for my cat may not work with yours. Assuming your cat has no health or digestive issues, try a small amount of the new flavor and see what happens.
I would say it depends on whether you are talking about dry food or wet food. With wet food there usually isn't an issue. With dry food, there might be simply because that's just a whole other ballgame, so then I'd slowly introduce the new protein even though it's the same brand