Are you looking for another parrot simply as a "companion" for your Hahn's Macaw, as a "mate" or because you want another bird? I don't believe in getting animals for other animals. I only think a person should get an animal because they want that pet, but only if they can afford to properly take care of it and have enough time to devote to giving it one-on-one attention.
Breeding is an exception, but I believe that a lot of research and effort goes in to properly breeding birds.
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.
I inherited a budgie (Bluey) when my grandfather passed away, and wanted to keep him with my budgies. It was a four month introduction process before they could share their flight cage together.
They tolerated each other but Bluey would rather human company over bird company.
My budgies - Yuki and Luna are different as well. Luna is fine to hang out with me, but Yuki barely tolerates human company. He'll put up with it though if he wants to hang out with Luna. (And by put up, I mean perching at my desk, Luna can be on my shoulder, but Yuki will stay on the desk)
Other birds though may get along if brought up with each other - despite size.
I love this picture of a Hahns and a Blue and Gold Macaw
From little to big - currently 6 Linnies; 2 Budgies; 1 BHP; 2 CAGs; 2 Zons; 1 GWM. Formerly in the flock: 1 LSC2 [fostered/rehomed] RIP: 1 budgie 1 WCP & 1 sweet Pan Am
There's a pretty good chance your Hahn's has chosen you as its mate & is driving away anything (the Greys) who might pose a threat to its mate & its territory. If that is so, it is not looking for a bird-friend & if you get a 4th bird, it will probably be rejected and you will likely have to add a 5th bird so the 4th one has a friend because the Hahn's just isn't that into it . . .
And that's a slippery slope that ends with more birds than you can support.
I speak from the experience of wanting a single companion bird, but ending up with 9, as I added friends for some of them, for the same reason you are considering a friend for your Hahn's.
I don't regret a single bird, but I admit that I didn't exactly do anything in moderation, so it would probably be better to do as I say, not as I do . . .