When I had allergy testing done, I was told there was a possible way of overcoming allergies. I am allergic to wheat and rapeseed oil. The Doctor told me to completely cut out these foods for 9 months (i.e. to not even have a crumb of wheat). After 9 months try a small piece of the food (e.g. one slice of bread) and see if you have a reaction. If there is no reaction, the following week try a little bit more (two slices of bread) etc and keep going that way. If however you get a reaction, then chances are you will not be able to get rid of the allergy. I think you would probably be able to overcome an allergy if it "developed" rather than if you inherited it.
I guess the same method would apply to other allergies - cut it out completely for 9 months, then try to slowly reintroduce it.