Interesting question, Dottie.
All my dogs have had some variety in their diet in as much as I have always added bits & pieces of 'people food', whatever I had around at the time, to the dog food I was using. Thinking about it has led me to recollect over 60 years of dog feeding...
When I was a child our family dogs were fed on a staple diet of boiled tripe, with leftovers added. Very healthy they were too. Then when I first had my own dogs I allowed myself to be convinced (by advertising? I can't remember) that dogs needed specialised foods prepared by 'experts', and I fed tins of Pedigree Chum with some sort of mixer biscuit, but carried on adding leftovers along with the occasional treat like an egg or tin of sardines.
I can remember being horrified when I first became aware of the existence of dry dog foods - it seemed so unnatural to me, and I felt sorry for the poor dogs that had to eat them day in, day out - but eventually I was persuaded, by vets and others, to switch to a dry food myself. I carried on with the additions though because I still felt sorry for dogs that were fed solely on dry food - and actually, I still do!
Looking back on it, that switch to dry was when all my dog feeding problems began, and so did the switching from brand to brand in an attempt to sort out the problems. Even with the additions, I was starting to see intolerances and upset tummies, things I had never experienced before, and my dogs never seemed to be as healthy as the remembered dogs of my childhood. So yes, by then I was switching the dry base of the diet from one food to another on a regular basis in search of Nirvana, sometimes with a result that was clearly worse and sometimes seeing an improvement - which always turned out to be temporary.
In a way, I'm very glad that the Little Cav turned out to be intolerant to every dry food I tried. That was what led me, in desperation, to switch to raw, and truly I can't see myself ever going back to a dry food. Home cooked maybe, like the dogs of my childhood, but not dry. No more temporary fixes, I'm sticking to 'real' food.
The Little Cav is now getting 4 different varieties of Nutriment and 2 of Natural Instinct in rotation, along with whatever else I feel like giving him on top.
Sorry, that turned out to be a bit of a long story. As I said though, an interesting question and it's helped me to clarify my own thoughts. And yes, I do believe dogs need variety, that's the one belief that hasn't changed over all these years.