Digestive issues

[finndog]

My boy Finn will be a year old in late December and has had digestive issues pretty consistently since he was around 4-5 months. His stools are almost always pretty soft (except first thing in the morning they're usually a little firmer) and he's had intermittent bouts of diarrhea.

He's also a very finicky eater and I can't tell if it's just because he's picky or if it's because he feels sick a lot of the time. Sometimes he'll eat his whole bowl when I set it out but other days he just grazes throughout the day. Other days I'll notice by 3 or 4 PM he still won't have even touched it. I know a lot of people on this forum are against letting their dogs "graze" but I've been letting him do it just for now because I want him to eat on his own terms and when he's up to it if he isn't feeling well. Probably I'll start being more strict about it when I find a food that he does well on.

My breeder had him on Nature's Recipe and he did OK on it but eventually started rejecting it. I switched him to Innova hoping he'd respond better to a higher quality food and he loved it but his stools got very soft. I then tried a grain-free salmon and sweet potato based food and he completely would not eat it. It was so bad that some days he just would not eat at all and then would vomit up bile because his stomach was so empty so I switched him back to Innova for a bit and now am trying Nutro. Innova is the only food that he never refuses to eat but I think it makes his stools the worst.

I brought this up with my vet a month ago and she did a fecal test for parasites and all came back negative. She told me to just keep him on the Innova for 4-6 weeks and not give him anything extra, so no bully sticks or treats. At about four weeks in he isn't any better, although I have slipped up with the treats a little–peanut butter on his kong toy every once in a while and pieces of apple for good behavior :)

Otherwise he seems to be in great health. His coat and skin look great and he's FULL of energy.

Any advice you can give me is much appreciated. Any tips on doing an elimination diet? Or tests I should demand from my vet?