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They just don't allow limits to be more than tripled with each increase. I tried and the system said it had to be up to three times the current limit and wouldn't proceed until I entered a correct amount.
Should be stated in the stickied 3x amex cli post.
Amex probably wont deny you for asking for 10k. Vast majority of customers have no idea what the policy is. Im sure they get 1000s of CLI req per day...