My youngest was diagnosed as a baby with an egg allergy, milk and soy protein intolerance and lactose intolerance. The egg allergy showed up on skin testing and he reacted with a full body rash. The milk and soy intolerance did not show up on skin testing, but he would vomit and have diarrhea until he was dehydrated.
I was told that allergies can change when hormones change: age 2, 3, 5, teenage, pregnancy, menopause, andropause.
At age 3 he was able to eat eggs finally with no reaction, he still does not like them though. At age 5 he was able to drink soy milk and we finally got up the nerve to trial him on milk at age 6. He eats everything now and has not had any issues. We still keep a watch out for anything interesting and I will watch closer when he starts reaching teenage years.
It is definitely possible with some people, but you have to be very careful with trials... they can be dangerous.