zoey, you didn't say how old your stallion was. That might make a difference in how well he receives a new stallion, and the age of the new stallion might make a difference, too.
I have two breeding stallions and a yearling colt, who would LOVE to be a breeding stallion, so I have to keep him away from the mares.
My two breeding stallions will kill each other if they are together. They will literally kill each other.
One of those breeding stallions will also try and kill geldings. And the funny thing is that I have two geldings that I got at the same time I got one of the stallions. They were all under a year old when I got them and they were pastured together for a few years. Then suddenly, the stallion became very aggressive and their normal play started producing bite wounds and blood, so they had to be separated.
Then I got a new stallion a little over a year ago, and he was about 8 years old. He can run with my two geldings or with the yearling colt and there's never a problem, but I just can't let him loose with the other stallion.
I don't let my stallions run with the mares during the summer. I've tried it, and the stallions will try to mount mares and there's so much kicking that I'm afraid a foal will get hurt.
I don't let the one stallion run with geldings in summer, either. Only in winter.
Yes, my stallions can see each other when they are in dry lots, but there's two dry lots between them. If I were to put them into adjoining dry lots, which are separated by cattle panels, they would bite and try to kill each other through the gates. When I put them into the pasture, the two stallions are tied out on 25' ropes. They can see each other but can't get near each other.
Everyone's stallions are different, so there's no telling what you might and might not be able to get away with. The breeder I bought my newest stallion from said he would try to kill geldings, yet I've successfully pastured him with them for six months last winter. I think part of the reason that was successful was because I put him in a dry lot next to the geldings all summer (when they weren't on pasture). So, they got used to each other.