The #1 problem is rough breeding of your hens. They aren't so finesse about breeding when they're competing with other Roos. Breeding injuries can be pretty serious. We didn't cull extra roosters fast enough in the past and one poor hen ended up with a deep 5-inch gash on her back. DH is a vet so her doctored her up, and surprisingly, she survived.
#2 problem is the dominant rooster (the cock) attacking the submissive roosters (this is where the name rooster comes from), so that they literally roost and may loose access to food and water. If that happens, they might start eating eggs and teach the hens to eat eggs too. We had that happen here over winter. Our dominant cock would only leave the roosters to roost on top the nest boxes. We didn't get eggs for months - even after taking the roosters out. Getting hens out of the coop on free range has resolved the egg-eating.
And sometimes it works out okay. Our other flock has a cock and a rooster. The rooster is a year younger, raised in the flock by a broody hen. They have minor conflicts over breeding rights, but the hens are in good shape and we haven't seen any major scuffles or roosting behavior from the young one.