I have enough space but they are penned
There are several posts on here where people say they have enough room yet the root of their problem is that they don't. How big, in feet, are your various coops? How big in feet are your runs? How are they connected? Photos can help. And how many chickens do you have and what ages are they now? How many total chickens do you expect to have in the future?
my Rooster is 5 months old and runs the coop, I want to add another Rooster but I don’t want them to fight or pick on each other or the new Rooster to bully all of my pullets
How can I go about that safely?
It can be hard to get chickens to behave unnaturally. If you put two males of a certain level of maturity together they will determine which is the boss. That is instinctive. But until they reach certain maturity levels age differences can go a long way in determining how they behave. You do not get guarantees of behaviors with any living animals, but a mature rooster is more likely to help take care of a baby chick of either sex than he is to harm it. You don't have a rooster yet, you have an immature cockerel. That makes it much harder to predict behaviors. An immature cockerel might be OK with chicks but is a greater risk to them.
What do you consider bullying your pullets? Again maturity plays a part on how they act but a male will mate with the females once certain maturity level are reached. That is instinctive behavior and is necessary for them to act as a flock. If you consider a male mating the females to be bullying then you don't need any males. When the males are immature cockerels and the females are immature pullets they are not going to act like mature adults. If you get baby chicks and raise them with the flock they will still go through that adolescent phase. If you bring in more immature chickens they will be in that adolescent phase. Your best bet to avoid the worst of the drama between a new male and females is to use adults.
But using adults causes another issue, that two mature males will determine which is boss. That means they will fight. If you truly have enough room it's quite possible they will work out a compromise where they work together to protect the flock. That generally means each sets up a territory out of sight of each other and each gets his own harem but there are some cases where they can work it out in tighter spaces. Even with a lot of room they could fight to the death but the less room they have the more likely a fight to the death is.
Siblings raised together that go through puberty often work it out, but things can get really rough between them and on the pullets as they go through adolescence. A baby male chick raised in a flock with a mature male can often work it out, but again adolescence can be rough. And when the cockerel reaches a certain level of maturity he may challenge the dominant male for control of the flock. They might work it out with neither being seriously hurt, or one might die. The more room you have the better your chances.
If we knew your goals and why you want a second rooster we might be able to help more. And knowing your specific size and configuration of facilities could help us come up with specific recommendations. Without that information my suggestion is to wait until they are all adults, bring in an adult rooster, and house each rooster with his hens in totally separated coops and pens so they can't get at each other. I don't know how well that might suit your goals.
