I would wait until your cockatoo gets through puberty before getting ANY other birds. Babies are easy, but the adults are a handful and then some (I have an Umbrella)--large cockatoos are the most re-homed birds of all due to their tendency to have very intense behaviors...Plus, they are dusty birds and their dander can actually cause respiratory disease in other non-powder down birds. Amazons can also get very territorial and aggressive when hormonal and that combination (cockatoo +amazon) could lead to many hospital visits if either decided to attack or even bite a sensitive area...which can easily happen--especially with two birds in the picture and the potential for added hormones, jealousy and aggression.
I would also be worried about what they might chew on etc---if they start chewing up your home or eat something poisonous and you aren't aware, that would be bad...cockatoos are prolific chewers. Additionally, the appearance of poop is very important, so I would suggest that you find someone who lives nearby and make then acquainted with the droppings-- ideally on a daily basis (but at least every other day). This is one of the first indicators of illness in many cases (color, consistency, bubbles vs none etc).
In many Amazons eye-pinning is one of their huge forms of communication, so without being able to see that, you could easily cross a line inadvertently and end up with some nasty bites. Body language is huge for cockatoos and Amazons.
Finally, sometimes birds get very aggressive and do not allow themselves to be touched-- this is rarely an issue in young ones, but as they mature, it is fairly common (at least during puberty and during hormonal spells). In the event that your bird became aggressive, I am concerned about how feather issues, a broken blood feather, or other injury would be detected. I imagine it would be very hard to tell, and in these instances, time is of the essence--in the case of a blood-feather, they can bleed to death very quickly.
They are natural masters of hiding illness and weakness, so a sick or hurt bird may eat fine and behave normally until things are very far along. The subtle cues are often visual.
Random thought:
You will definitely need to find a way to contain your bird while you are cooking etc, because if he/she comes flying into the kitchen with hot pots and fire on the range, that would be very bad as well.
