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There is a button, if you got NPSL, that you can punch in a particular amount and it will let you know if you are approved up to that mark or not. I have hit the button twice since I got my card and I can put 5k on it. Just try your luck when you get your card and register for online access. If it says something like 2.5 or 5, then you can just push through multiple payments in a month.
I am a bit confused because I called AMEX back to see when my card was scheduled to arrive (expedited shipping) because I live in a walk up building without a doorman, etc. This was yesterday and she couldn't see any new Green card on my account, only my old Gold card from '06 that was barely ever used.
If you go application status online it says IN PROGRESS, but I was told last week on Friday by an AMEX rep that I was approved for the card and that it was being mailed to me. This was after they got on the phone with Chase Private Client to confirm my new address, etc. The new accounts or whatever department she was trying to transfer me to is also closed today for the holiday. I suppose I'll just have to wait until tomorrow to find out what is going on, but found this to be a bit weird.