I only had the MC and Amex so far so I just applied for the Visa. Got a message that app received and they will contact me within a week....
Holding my breath...
I thought it was posted that the card's designation didn't matter. Ie, if you had a personal card (regardless of whether it is/was the Visa, MC or Amex) you couldn't get another personal card (even if it was a card of a different designation). Although you could get lucky and sneak through the cracks.
As a related question, what if you have two AA accounts that haven't been merged. If you've gotten the bonus on one AA account, could you apply for the card again using the other AA account?