Foods actually can be switched (varied) without impacting a dog’s digestion. That is more myth than reality. Why? There’s money in this myth: the dog food companies don’t want you switching away from their food. If you vastly change what they eat (say, put a full plate full of fat down as dinner) you may have a problem, or your dog has a sensitive stomach due to some problem, but if it’s just the same kind of ratio then most dogs are fine.
In fact, it’s beneficial to a dog if you rotate their diet. This is called “diet rotation”. Here are some references:
There are very few dogs to be known to actually have an issue with rotating their diet, and you can always do so by gradually adjusting things, or even just changing what’s in half of the bowl if you experience any issues.
So, on that note I would switch it up if your dog likes new foods. Your dog may feel like he or she is missing some nutrient, or may just have preferences as animals and humans tend to do. I always recommend a fresh homemade diet, but even if you do not feed one you can always add real foods that are safe for dogs to the bowl, such as fresh vegetables or what you make for dinner that a dog can eat, that add some variety.