Are your hens Buff Orpingtons as well?
Getting more hens is not a solution unless you are prepared to build another coop and run for each male you wish to keep.
The reality is males very rarely fight over females no matter how it may look. What they do fight over is space and resources. The rooster with access to the most resources gets the pick of the hens by and large. The hens pick the rooster they wish to further their genes with. What attracts hens apart from the roosters stunning looks

is how much money (resouces) that rooster has access to. If you are no longer free ranging then the total resources are what's in your coop and run. I found about an acre per group kept resource conflicts to a minimum when keeping multiple males.
How did having a broody hen hatch chicks go?
My view is letting chickens carry out their natural behaviour as much as possible has benefits for the chickens and the keeper and having hens sit and hatch offsprin is about as natural as it gets.
Of course if one does let broody hens sit and hatch then it is inevitable over time that one gets 50% of each sex. This is your chance to not have to risk bringing in sick chickens from outside your group and not have to deal with all those introduction and integration issues many people get trying to introduce strangers to a stable existing group.
Eat the cockerels and hens that you don't wish to keep. Keep the cockerels until they become a problem, if they become a problem, rather than rehoming them. If they live in the group for six months, or even a year or more then compared to the commercially raised chickens they will have had a far better life.
This will allow you to take some time to assess which males are going to fit into the group and which are going to challenge your senior rooster for the resources he has access to; your coop, run and all the hens.
If you can't find it in you to kill the chickens you cannot keep then find someone who will do it for you. Lots of farmers leave the slaughtering and processing of their livestock to outside agencies.
In general the chances of keeping 4 males in the space you have without constant fights, pestered hens and stressing the group are close to zero.
More hens is not going to solve the probelm and may make things more difficult than they are.