3 is still too many roosters for the amount of hens. 1 rooster is all you should keep for that amount of hens, or you are going to run into problems later.
How long have you had the new hens, and how old are they? How old are the preexisting birds? How long have the two groups been able to see each other?
No you can't simply throw them together and expect them to get along. Your existing birds, even the girls, will not tolerate simply having new intruders in their space.
Ditto Dos^^^
The 'rooster' to hen ratio of 1:10 that is often cited is primarily for fertility efficiency in commercial breeding facilities.
It doesn't mean that if a cockbird has 10 hens that he won't abuse or over mate them.
Many breeders keep pairs, trios, quads, etc ....short term and/or long term.
It all depends on the temperaments of the cock and hens and sometimes housing provided.
Backyard flocks can achieve good fertility with a larger ratio.
Here's some tips about.....
Integration Basics:
It's all about territory and resources(space/food/water).
Existing birds will almost always attack new ones to defend their resources.
Understanding chicken behaviors is essential to integrating new birds into your flock.
Confine new birds within sight but physically segregated from older/existing birds for several weeks, so they can see and get used to each other but not physically interact.
In adjacent runs, spread scratch grains along the dividing mesh, best if mesh is just big enough for birds to stick their head thru, so they get used to eating together.
The more space, the better. Birds will peck to establish dominance, the pecked bird needs space to get away. As long as there's no copious blood drawn and/or new bird is not trapped/pinned down and beaten unmercilessly, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.
Multiple feed/water stations. Dominance issues are most often carried out over sustenance, more stations lessens the frequency of that issue.
Places for the new birds to hide 'out of line of sight'(but not a dead end trap) and/or up and away from any bully birds. Roosts, pallets or boards leaned up against walls or up on concrete blocks, old chairs tables, branches, logs, stumps out in the run can
really help. Lots of diversion and places to 'hide' instead of bare wide open run.
Good ideas for hiding places:
https://www.backyardchickens.com/threads/a-cluttered-run.1323792/