American Express was on record stating that there is a limit of 4 credit cards and 10 charge cards per person. These limits count personal and business together.
There are multiple reports of people getting approved for their 11th or even 12th charge card. (1, 2, 3) It’s possible they disbanded the limit altogether or they may be other factors allowing people to bump over the limit a bit.
Separately, the limit of 4 credit cards is also YMMV with some people getting approved for 5.
Amex typically does not hard pull existing cardholders who apply; it can’t hurt to apply for another card and see what happens.
