EDIT--
Forgot to mention the importance of time and relationship building. Parrots move in slow-motion, so before doing any of the things below, try to build trust and take it slow. Birds are obviously a comfort zone.
Try to find what else she enjoys and see if you can make her like you better by associating you with favorite treats etc.
I don't know about your particular bird, but you might look into the "model-rival" method (which would use your other birds as examples for human interaction). It can work with greys and cockatoos, but I haven't tried it on others. If she enjoys being around other birds and attends to what they are doing, this might work...and the reward could be a treat in some cases, but because it sounds like it is their interaction that she wants, you could leave one of your 2 other birds on the playstand (while one models- preferably the one whose behavior with humans is best)and then place bird #2 on the playstand when it does what you want..over time, you new bird might make the connection and follow the pattern (stand on hand for 10 seconds, let human touch head, go to playstand with my bird friends)
If being with other birds is reinforcing to her, you might be able to use that as a reward. It would take time to work your way there, but basically, some time with you= time with the other birds right after. Side-note: If you try that, you would only want to give her that time after spending time with you though, otherwise the association would be difficult to establish. It would have to be done in baby steps. Increments would need to be short at first (both for special human and bird interaction)...and there would need to be standards for behavior, but I don't know what she does when you try to interact with her, so it's hard to guess.