I do not believe there is really a "maximum" for any food (besides sweets, which are not "a food), especially egg-whites, which contain no cholesterol.
At one point of my life, I was eating 36 eggs a day. 30 whites and 6 yolks, everyday. Yet, look now, 7 years down the road I got cholesterol that is very very low, but I still eat over 15 eggs a day at times.
Mr.X