This is what Dr. Wendell Belfield says on the subject of changing foods:
"Very often when a pet owner changes pet foods the pet, dog or cat, develops diarrhea and sometimes vomiting. This is not necessarily the pet food, but rather a subclinical form of inflammatory bowel disease."
Now the thing is that quite often (almost always) food allergy is a big part of IBD, so the ingredients in the foods one tries are very, very important.
Rotating foods freely is possible only if none of the foods used contains any allergens for a particular animal.
For cats that don't suffer from food allergies, rotating foods is easy and they welcome the change. They love the variety. With allergic cats foods have to be selected most carefully, and sometimes rotating brands is simply not possible. Serving different flavors from the same brand is the best one can do.
Digestive upset is always an important warning sign, so if a cat develops digestive problems from several different foods then either the same kinds of ingredients are responsible, or the cat's body is just not producing enough digestive enzymes to deal with the foods.
If the cat is allergic, the safest thing is to avoid the foods that contain the allergens. If the problem is below par digestion, then the best thing is to find one good, allergen-free food and doing a slow, careful food change that starts with no more than 1/2 tsp of the new food.
For such cats nutritional treatment can be tremendously helpful.
If you can't get the runny stools under control with different food, the reason might be that your cat's intestines are inflamed. If that's the case he would benefit from a short course of anti-inflammatory medication and carefully selected food that is free of all the major allergens.