First off, has he had a stool sample taken at all? Certain bugs that cause intermittent diarrhoea/loose stools are fairly common in pups and although a stool sample can be pricey (think ours was about £150.00) it's worth it to eliminate any nasties, especially if your pup isn't carrying enough weight.
Our boy, now nearly 1, had similar symptoms as a pup and turned out to have a nasty campylobacter infection, the other thing the vet was considering was E-coli, but there's also Giardia and a couple of others that should be eliminated. Some/all of these can be passed onto humans without proper hygiene and husbandry and children are most at risk.
In the meantime, either put him back onto the food he was tolerating or take him off commercial food completely and just feed him on fresh cooked white fish or chicken (obviously not chicken if you think he's intolerant though) while you are sorting the problem.
He will need small feeds more often than normal to get enough food into him, but barring any underlying medical condition, he should gain weight once his gut is settled. My pup was on 8-9 meals a day of oven baked chicken (complete with skin for the fat content) and regular probiotics at the same age as yours. He was on just chicken for a good few weeks and it hasn't done him any harm, as he's a strapping 28 1/2" to the shoulders and fit as a fiddle these days. 
You can buy probiotic paste, such as Canikur here to help repopulate his gut with the right bacteria. My boy had the brand I linked to (we had it from the vet at first, but found it cheaper online) he loves the taste and will happily just lick it off his bowl. I keep it in stock now, as it's great for sorting minor stomach upsets in dogs too.
Then, when he's ready start by just adding literally one piece of your chosen kibble to his meals and build it up very slowly from there. Personally, I'd go for something grain free, as in all grains, including rice. They will be more expensive, but well worth a try, as a lot of dogs can't tolerate grains.
Have a look on this site to compare ingredients and costs.
An alternative would be to get his digestion settled down and try him on raw. You could go for one of the prepared brands like Nutriment if you'd rather not deal with bones and raw meat yourself.