DIRECT QUOTE FROM AMEX <<No pre-set spending limit does not mean unlimited spending. Purchasing power adjusts with your use of the Card, your payment history, credit record and financial resources known to us, and other factors.>>

That said it is my opinion that people who have a good credit and good history with amex seem to be able to go 1.5 times the pervious highest amount owed to Amex. By highest amount owed to Amex I do not mean your statement balance but your total exposure to Amex. This is your previous balance plus current charges. Once again this is my opinion and the rules change the more you see these things , , after a dollar $ign.