I can't seem to find 3 different brands and proteins...where all goes well all the time.
Is it even possible? I have one who will eat anything, and can. She never has ANY problems, with the exception of constipation, which has been solved with pumpkin. Some foods, fed too often (Weruva, Soulistic and Nature's Variety) seem to give her extra constipation trouble, but I keep those less than once a week in her rotation for that reason. When the NV is gone I won't be buying it again.
Then, I have one who doesn't vomit or have constipation, but she has so little interest in food at all that I despair sometimes. I guess I'm doing okay with her, she never seems to lose any weight, though she is extremely slender. She is not a big cat and weighs 7 pounds.
And of course you know my struvite girl who has been unable to handle any variety at all. I don't know if that will ever change, nor do I know how much of it to blame on years of c/d kibble. I just have to pray that the food she is on is not lacking in anything, and never has a recall.
I didn't mean to make this about me, sorry about that. I guess I am just trying to illustrate that there is no one answer for a multitude of cats, unless you are the type who doesn't care about things like this. The type, of which I am sure we all know many, who dumps a bag of "whatever is on sale" in a dish, tops it off once in awhile, doesn't think twice about it, doesn't notice what goes into the litter box and thinks finding piles of vomit is normal.
But, back to the topic, I have two who eat a variety of brands and proteins, rotated daily, if not every meal, who have no problems at all, and one who cannot eat ANY of the foods they eat, can only eat one food.
No, that's not what I wanted to say. The only way to narrow it down is to keep a cat journal. You list every cat. What you feed them, what time you fed them, and the results as far as what each does in the litter box, or vomits.
Then after you've been keeping records for a while, you go back over everything, looking for patterns. Hopefully, you find common denominators, so you know which cat can eat such and such and which cat needs to avoid it. And so on.
That's the only thing that works for me, anyway. Of course I have only 3 now, but I did it with four too. I know you have more than that, so it will be a bigger challenge.