I know a lady who had her three all put down together. A pony in her thirties and two horses in their twenties whom she had had for years. They all had some medical conditions and she was struggling financially. I thought at the time it was a very brave and selfless thing to do. Rather than pass...
You don't mention where in the herd the 'bully' ranks. Sometimes lower rankers can be worse for having an issue with another herd member than a true leader/dominant. All to do with their own status and trying to keep it. If it is a problem, move him. A bigger herd does not necessarily mean more...