When I didn't know any better, I put my young cockatiel and GCC together in a cage after they became very close. They were 4 and 3 months old and they've been growing up like siblings.
But now I have them in separate cages and will keep it that way. They spend time together when they're outside of their cages, but I think it's safer to keep them separate when I can't supervise them.
Hopefully someone with more experience will post, but from my currently-limited experience with Greys (I've only had my baby for 6 months) and zero experience with Amazons, I don't think it would be a good idea to house them together. It's my understanding that Amazons are quite different from Greys in typical behavior, and I feel like it could get dangerous if they're kept in the same cage.
Your grey probably wouldn't appreciate having a new roommate.