The types of protein can make a difference as well. Switching from a "white meat protein" to a "red meat protein" can affect dogs.
Alice doesn't do as well on chicken as she does on lamb/beef. Zoey, is a garbage gut, will eat anything with little or no effect.
Switching too fast is never a good thing, I've taken two weeks or more to switch a food. (hence I don't do it very often and really think about it before I do)
Sometimes the fish based protein foods help with the skin problems and sometimes yogurt does too. (yogurt is a maintainence issue though, once you start you keep doing it as it takes awhile to start noticing effects, like good ears, skin etc.)
*there was one time where Zoey stole the loaf of bread from Alice that Alice stole off the counter......they are both on grain free and .....well, bread is one big grain.
Zoey ended up on boiled chicken and rice with a little pumpkin for a few days
Let me tell you how fun it was to wake up to a dog that "exploded" in the bathroom.....well at least it wasn't on the carpet.