I haven't seen this asked yet: is he gaining weight at an acceptable rate?
My 2nd son has a severe dairy allergy and was able to nurse after I removed all dairy from my diet. However, he still spit up what seemed like more than he was taking in. Every feeding. But he was fine medically and was gaining well, even though it was hard to believe that any stayed in him at all. If your baby is gaining well, just be patient (I know it's hard). And keep lots of burp cloths on hand. I don't think I was ever without one in all my waking hours with my son.
As others have mentioned, allergy testing could be a very good idea. Dairy and soy are among the top 8 allergens.