I agree with Ridgerunner (a highly respected poster) your fighting will not be affected by adding more birds to the same area. Many people are quite surprised at the violence roosters can produce.
I just recently visited a place where there were multiple roosters, I counted 8 and there could have been more, in a flock of hens (didn't count). And Shaddrack must have something similar in a pretty much totally free range situation, so it can be done. However, this is a multi-generational flock. There are older birds, and younger birds, bigger birds and smaller birds in a lot of space, with a lot of cover, and hideouts.
Thing is, that is a totally different societal dynamic, that a 50/50 flock mate growing up together society with no older birds, and no bigger birds to thump some respect into the juvenile cockerels. There tends to be a theory that growing up together will lead to tolerance, and it does with a lot of pets. However, with chickens I really don't think it has any positive effect. The juvenile cockerels are bigger than the pullets, and running wild and full of hormones, and fighting. Fighting that can get ugly.
I recommend, reduce your rooster flock anyway that has been mentioned. You do not need to do them all at once, but keep thinning it until, you get some harmony in the flock. Let this flock grow up, get some society established, then next year, you cam probably increase your rooster level if you want.
To keep roosters, you need a sharp knife and the ability and will to remove problem roosters. That is animal husbandry, and it is considered kinder than letting nature take her course.
Always solve for peace in the flock, fighting roosters constantly cause commotion, draw the attraction of predators, and is very hard on the pullets, even if they are not in the fight.
Mrs K
