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Given the size of the tank is appropriate, there is no reason why these species cannot be kept together. However, there is a few more issues than just the tank size. Cacatuoides typically are more at home in slightly alkaline water, for example. Aggies are not.
And then there is the matter of individual personalities. Some fish are predisposed to be extremely aggressive to anyone else in the tank. That may be one of the cacs or one of the aggies. you just have to try it to know for sure. But it is likely that they will be OK if they have the space to establish their own territories.
They will not interbreed. 2 completely different fish.