If your hahn's attacks your CAG's, there's a very high chance he'll attack any other birds whom you attempt to introduce to him. Some birds just don't like other birds. It is possible that, yes, he may get along better with a bird more similar to him. Or he may hate it just as much, if not more, than your CAG's. The thing is, if you get another bird and your hahn's gets along with it, that bird is your responsibilty. If you get another bird and your hahn's does not get along with it, that bird is still your responsibility.
Ultimately, if you choose to get a fourth bird, do it for yourself, not for your hahn's. And if they get along, that's just a bonus.