Offer them some cat grass to settle their stomachs while you search for the right food. I feed Kirkland after trying every brand on the market. My cats all like it, the nuggets are small enough they don't cause problems and it lasts a long time. I do mix Purina One with it during the wintertime to help add bulk to their bodies as they are inside/outside kitties and it gets cold here at night.
It is up to the pet owner to figure out what formula they need to use for their cats and the individual cats needs. Talking to vets will help, doing research, but don't believe everything you read about pet food, if you are in doubt about the food you are feeding, then write to the company and ask them directly. Generally they will bend over backwards to help you out and even send you cat care kits and coupons if you make the effort to write to them. That is how I found out about Purina One willing to pay some of my vet bill if I turn in weight circles from the bags. So many circles, nets $25.00 to my vet. The check is written out to the vet, not to me. It has been a great help this year, and I hope they continue this program next year.