To the OP, if your vet thinks this is an allergy how about an elimination diet? If you just cut out grains and things are no better in 12 weeks you will have to go with an elim diet anyway. are you sure this is not an environmental issue?
Absolutely switch foods if you think this one is not working. I'd just choose carefully.
It is interesting to me that so many dogs on yt have tearing blamed on food. I'm not saying it isn't happening, but it seems this is not an accurate representation of what the average vet sees...
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If you don't like SD, don't feed it. Simple.
Whether or not meat is the first ingredient after grains are added is not important to me. I would not want and would not let my dogs eat that much meat. And the more Ellie's homemade diet was changed up/rotated, the more issues we had.
Basic nutrition is easy. Nutritionally biochemistry and physiology are not. If it is really that easy then more people would have PhDs in this field.