I love cockatoos...although you have to watch it. They are often known as the 'ADD' bird. They are best in a house where there is constant activity, a display bird at a petstore, or even in the waiting room for an avian vet. They need A LOT of attention...and if they don't get it, they express their frustration in other ways. Either by destroying things, biting, screaming, or plucking.
My sister-in-laws family use to have a Cockatoo. It was a family of 6, all of which are very familiar with how to raise and treat a bird. Anyway, it got to a point that the bird wasn't getting enough attention. It would bite, chase you to attack your feet, and scream a blue streak.
If you can give the cockatoo the attention it needs along with your two other parrots....they can be awesome feathered kids. Otherwise...?

Nevermore