Here are two quotes from people whom I highly respect. They are about dog food, but I am assuming it would apply to cat as well.
From the Great Dane Lady:
"Why Can't I Mix Brands of Dog Foods? It is very important NOT to mix different brands of dog foods together, or even mix the same brand name, but different products within the line. An example of this would be mixing an adult and senior food of the same company, or mixing two brands i.e. Innova and Eagle together. Because every type of food developed by each company is "designed" nutritionally on a nutrient matrix system of vitamins/minerals/amino acids, it is critical to maintain the integrity of that nutrient panel in order for the food to be balanced. When you move one element in that nutrient panel, it effects all the elements and therefore adjustments must be made in order for the food to be re-balanced. When you mix two foods you will cause excesses and deficiencies in certain nutrients as well as disrupt the delicate balance of the food, especially the minerals composition which is critical to the body's metabolic and skeletal systems. These deficiencies or excesses may not be evident immediately in an adult dog, but they will manifest in a slow deterioration of the animals health and reproduction capabilities. As we know from past experience, it does not take long for the body to exhibit dietary problems in a growing animal."
From Lilian's website, The Dog Food Project, under the heading Myths about Feeding and Nutrition:
"Mixing different dog food brands will improve my dog's diet - This misconception seems to originate from dog owners feeling guilty about the type of food they feed or those who follow their own ideas for "improving" their dog's diet without doing any research. Every brand of dog food is following a specific formulation and philosophy developed by the manufacturer. They are all formulated to supply a balanced amount of nutrients in a ration of a certain size, based on the body weight of the dog. When mixing different foods you run the risk of your dog getting either not enough or too much of certain nutrients."
I raised the question because most people in this forum seem to avocate mixing brands for a long term, which is very different from what I have been told. Of course, we all do what is the best for our critters, and we don't do things just because we are told to.
By the way, mixing food for transition period is a different story.