angels,
What about Stella & Chewy’s? Excellent food. They make raw dehydrated medallions that are meat & bone based, with organic fruits, veggies, seeds and do not contain any of those ingredients you listed. In fact they don’t include any starches or grains period. This is great brand and dogs seem to really love the stuff. With a maltese it would be pretty affordable to feed, vs a medium or large breed dog. They’re easy to feed too, can be fed either with water or dry, shredded/broken into quarters/whole. Try the DuckDuckGoose — has duck, turkey, goose. No chicken.
Also, I highly recommend Timberwolf, have fed it for years. The Platinum Ocean Blue (fish based) has sweet potatoes (which you said are fine), but no peas, white potatoes, or grains. It has sweet potatoes and garbanzo beans (chickpeas). It’s nutrient dense, very high calorie; so you would be feeding very little especially to a tiny dog. I’d recommend introducing this food slowly over 1-2 weeks to ensure tolerance, as it is very rich and contains ingredients not commonly found in other foods and all at once.
Aside from these, rather than trying a whole bunch of commercial foods, I’d try first pinpointing what your dog CAN handle by feeding ONE protein and ONE carb. And I’d try to make sure that something is an actual allergy vs an intolerance or upset, since they are different. I’d try boiled turkey or cottage cheese and sweet potato OR oats (since you know your dog is okay with either). (By the way, many dogs are intolerant of lactose & milk, but fine with yogurt or cottage cheese.)
