There have been theories floating around the community for a couple of years regarding how many American Express credit cards (not to be confused with charge cards like the Gold, Platinum, and Green) a single person can have. Depending on who you ask or where you look, you’ll find some consensus at a limit of either four or five.
New evidence is emerging on Reddit and in private channels that suggest a limit of below five cards is caused by holding one or more charge cards with Pay-Over-Time enabled. So, I’d like to again suggest that you un-enroll from Pay-Over-Time at this link to free up more slots for AmEx credit cards, especially if you’re close to or right at the five-ish card limit. AmEx also sends gifts for charge cards not enrolled in Pay-Over-Time, so double win.