Awe they can hang out together? How precious! I wish more of my birds could. The Senegal and sun conure chase eachother around striking and I'm too afraid of injury (ive seen green cheeks bite the beaks off of other green cheeks, so similar sized birds can still hurt each-other ):
But my sun conure was raised with my cockatiel and the cockatiel is harmless and passive so she can hang out with the conure. She can also hang out with the lovebird but the conure wants to kill the lovebird (the lovebird loves all), so not all three together.
I have not really tried the caique playing with any of my other birds as they have a reputation for killing other birds. I do know my sun conure hates her guts as well though. Not sure about the Senegal but I doubt she had the patience.
The cockatoo..... It's out of the question--- that big bad beak!