Your situation is very similar to my cooped chickens. My 9 hens and 5 roosters were raised together as chicks. Breed can make a difference in temperament of course. We chose mild mannered breeds, cochin and orpington, but one of the roosters is a rhode island red mixed with an old english game named Ruby. Ruby was smaller but less laid back so he had established his dominance early on without any fighting. Every now and then they might peck at each others combs and give a few scabs but there have been no all out fights.
Our problem was even though Ruby was dominant, he wouldn't stop the other roosters from mating with the hens. So the poor hens started lost feathers from their back and neck from all the mounting. they started hiding in the nest boxes rather than free range even though they were not broody just to avoid the roosters. Fortunately your rooster to hen ratio is a little better
We finally built another coop for the big mild mannered roosters who we call the bachelor roos. The four of them get along well, but now that they are separated from Ruby and the hens, one of the orpingtons insists on fighting across the chicken wire with Ruby. The two groups are not allowed to free range at the same time.
In other words it might be possible to house them together, but a change in situation could upset their hierarchy.
