Hmmm... I am a bit confused. Did you have two roosters in the flock, and then add this one? Is there, was there any rooster fighting? If all the roosters are overbreeding, they are in competition for the hens with each other. This generally leads to fighting until the roosters get the hierarchy worked out, but can reappear.
Roosters breed chickens to show dominance. Now if your roosters are young as in less than a year old, the sexual drive is intense, and either the hens that are not getting overbred, probably fall into two groups, either they are older and more aggressive, and he is not yet dancing, his technique is poor, and they are not having it. They won't squat for him,he is a bit intimidated, so he can aggressively get the ones he can breed, or the hen is agreeing to it, so there is no challenge and he does not have to keep proving himself. Sometimes a rooster will pick a favorite, and get that one often.
Of course, lack of space and lack of hideouts can have an effect too.
However, the main point of your post is that your flock is not peaceful. When tension start to rise in my flock, culling is the answer. Cull one rooster, wait a week, if things are better, ok, if not, cull again maybe looking at your hens closely, besides looking at the roosters. It is worth the difficulties of culling to have a healthy and happy flock. Not all birds will fit into your set up.
MrsK