This is not true. I've had multiple roosters most of the last 20 years and have only had a few fight. Some were hatch mates, some were father/sons. I've never had rooters fight so much they drew bleed, even when they did squabble. Don't know what I do that's unusual. I give my birds lots of space and don't tolerate any human aggression and don't make my birds pets, that's about it.
I agree with donrae, they most likely will not fight enough to draw blood. They will likely spar each year, usually in the spring, fighting over who will be the Alpha. As long as there is enough room for the loser to run away, the winner will be satisfied with chasing them all over the place and then leaving them alone. The winner may chase the loser off for a couple of days after that, but then things will settle down and get back to normal for another year.
I've also never had roosters draw blood from each other, even when they spar. They do pull out feathers, though! We also have lots of hens per rooster, lots of room, and we do not allow any human aggression whatsoever, and we do not make pets of roosters, either.
We have.. um... (counts on fingers)--seven roosters right now. We've had as many as 16, but most of those were in a bachelor pad (meat pen) at the time. Again, no fights severe enough to draw blood. Ours are not all hatchmates or fathers/sons.
What may happen with your flock is that your hens will be stressed and over-mated because the ratio of roosters

ns is too high. This can impact their egg laying, behavior, and disease resistance. The usual recommendation of roosters

ns is 1:10 or so. You can get away with fewer when you just have one rooster in the flock, but the more hens you have when you have multiple roosters, the happier your flock will be.