I know I will get trashed for this but hey never cared much what others think.
EVERY rescue I have ever had did best on Pedigree. We found that by breaking feedings into small meals multiple times a day and slowly adding fresh food into their diets we greatly reduced the days of cleaning nastiness.
Many big name kibbles are just too rich and a dog with a trashed tummy may not do well on raw food. The detox effect caused by raw can put more pressure on an already compromised system.
I found feeding multple small meals and gradually introducing raw meat berries and eggs cut recovery down considerably. My own dogs ate Pedigree for years and did well. Same diet. Smaller amount of kibble. Fresh fruit berries meat veggies and eggs.
Years ago, only thing we could get our rescue to eat was Old Roy, with a raw egg on top. She did well on it, not that I feed it to my dogs now but sometimes the oddest things work.
"If there ever comes a day when we can't be together,keep me in your heart, I'll stay there forever." A.A. Milne