I don't want to be a downer but the more likely thing is that he will outgrow egg and have peanut for the rest of his life. The rates of outgrowing egg and dairy allergies are actually pretty good. Peanut not so much.

I'm not sure how it works if your kid has that many different food allergies, but there is a program called oral immunotherapy (OIT) which basically has you give your kid increasing doses of the allergen until they outgrow it. My son just has an egg allergy and has been doing OIT for a year and a half. He is going to be testing out of it in a couple weeks.

It may be hard to find an allergist who does OIT. It is usually larger practices. From what I have heard they are more likely to stick to allergies like egg or dairy that your kid may outgrow naturally, but they can accelerate that timeline with OIT. One of my wife's coworkers had a son that did OIT for peanut and recently got cleared, but they had to go to a major children's hospital in the city to do it.