You have no idea how a new parrot would impact these relations. The new bird could change things a lot (including your quaker's alliances). As I said, there is no way to know that they will get along with each other, let alone, your family (even if they don't, they can still change the dynamic within your current parent/family situation). On top of that, mixing a sexually mature quaker with an immature grey could be very bad- especially if the grey's /Amazon's opinion changes when hormones kick in, and even before that, they could bite your quaker in an instant..
I would keep their cage's separate at least the first month and if they don't end up getting along I could give away the Amazon to someone I trust will take good care of it.
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Sorry- I can't support that as a reason to justify getting one---if you don't have the time or ability to devote to them in the event that they don't get along, then you really are not in the position to get another-especially given how much your life will change and the fact that you KNOW you will be leaving them in the next few years. These animals are more like people than pets- with the IQ of a 4-year-old, that's a lifetime of trauma just to make a person happy...You know?
I understand that everyone sees things differently, but these animals exist for themselves, not for our pleasure, and we already deprive them of their natural habitats etc....The least we can do is give them the life-long bonds that they seek out and obtain in nature. They bond tightly...they do not leave their families for long periods unless they die. Giving one away on a whim is like giving a kid away --they might get food, water and shelter, but they are going to miss the people they are attached to, and the environments they know.
I don't understand the rush when you aren't in a good position to adopt and you have your entire life ahead of you to do this...Why not wait when you know it would be the safest (and kindest) thing for the animals? You also are negating the fact that your quaker is already going to have to deal with your absence, and that WILL be hard on him. You are his flock...Why bring another bird into that until you are settled ---best case scenario, he gets along with your other bird, gets attached to you and then you leave him (at least, in his mind...) We already discussed the worst-case scenario...and we don't agree there.