Let's review:
You have the smaller, more timid, overly sensitive African grey species and you want to put it with one of the larger, notoriously unstable, extroverted, and loud cockatoo species?
You've got some reading to do……
All About Cockatoos - MyToos.com
When you're done reading, and you still want to do this thing, read it again.
In the right hands, and umbrella cockatoo could be a wonderful thing: and I can count the number of people with the right hands on the fingers of one hand-- there's a reason there are so many of them up for adoption on Petfinder and it's not the birds' fault. Nobody does any research anymore, and it annoys the living hell out of me when that becomes dangerous.
If you absolutely insist on putting in African grey in the same household with a cockatoo {with 100% separate cages}, you want a bare eyed cockatoo {. Their intellect and emotional functioning is closer to an African grays than any of the other cockatoo species, but don't count on it applying to every single bird of that particular subspecies. I'm only speaking for the ones that I've known, and every bird as their own particular personality nuances}
Onto the next question..............
As for the Amazon question, there's a pair on Petfinder right now for adoption {I think it's a Congo African grey with the Amazon in that case, but not 100% sure}. Now time to review Amazons:
Wonderful birds until overly excited with any particular emotion or even hyperactivity – then things get hormonal and possibly bloody. This also theoretically applies to pocket parrots, a.k.a. pocket parakeets, a.k.a. parrotlets(think of them as miniature Amazons with burrowing tendencies). You already have an Amazon, so you probably already know this – or will find out the hard way at some point.
Congo African grays will take control of absolutely everything! You don't have a single say your own house anymore, because the bird must be obeyed. The only time they're not telling the other living species in the household what to do is when they are co-conspiring against the humans. Have you ever been double teamed by a parakeet and a CAG? Let me introduce you to part of what my life is like:
I use voice recognition software to type. I leave the room with my mom to watch TV. The gray makes arrangements with the budgie to take my voice recognition software over. The gray turns it on by voice. Then, the budgie proceeds to fill up the screen with words – an entire hour worth of screens before they were caught-- with the words "itty-bitty little birdie birdie birdie itty-bitty itty-bitty little birdie......" which were the only words the budgie knew, because that's pretty much the only thing anyone ever said to her directly..... Which is how we figured out her involvement, a.k.a. the little bird that didn't talk.
Those were the earlier years. We'll call those the baby steps years, before the CAG learned how to summon the ambulance for his own amusement. In fact, one of his favorite hobbies was figuring out how to lure people to the door and prank them. What happened behind closed doors was epic, if only it happened to someone else. It happened to me.
Dear long-suffering Dr. Kupersmith, would ask every once in a while who was in charge – the people or the bird.
I always answer, "the bird"
You'd think he'd get tired of asking............