two years ago when I raised a group of geese, I noticed one gander was head gander and did all the mating attempts. So, yes you can have several ganders, they could fight here and there, but not to the extent chickens do. But if you want to raise pure breeds, I'd separate them by breed. You COULD have them bonded to each other, but that won't prevent a goose from accepting matings from other ganders in a mixed flock. It probably isn't very high an incidence rate, but it can happen when being kept in a group. But that might not trouble you if you can recognize the crossed babies and have an outlet for them in the fall.
They rarely mess with the chickens unless they get too close then they just lower their heads and the chickens know to stay away. 