Woohoo! Now that he is gobbling up his new food, he'll put on a bit more weight yet!

After he is off the tuna, if that happens - I wonder if some canned salmon would be ok? It comes packed in water, and is a very oily fish anyway.

Or there is Omega 3-6 oil in a pump form for dogs. I use it for my two cats as capsules every morning would be a hassle. But you could use half a pump mixed in with some wet food. See what your vet thinks.