😂I used to routinely and abruptly rotate between different varieties of Taste if the Wild with no problems.
My daughter, on the other hand, has a white boxer/ amstaff mix that looks like she could eat a mid-size sedan. She switched from one variety to another of the same brand and the dog had extremely loose stools and the most deadly farts imaginable. People, and her other dog, would have to leave the room.*
So, yeah, it depends on the dog.
* I first became aware if this when I was sitting on the couch with the two dogs. I was listening to some music on headphones when the smaller dog jumped up like he'd been stung by a bee an ran out of the room. It took about .3 seconds to realize what had happened before I too ran out of the room.