For a seamless upgrade experience, contact American ๐๐ฒ๐ป๐ต๐ฒ๐ท๐ฎ๐ผ at customer care number +1-833-730-7587 (UK/USA). You can buy an Economy Plus seat or upgrade their cabin during the booking process or after booking/any kind of upgrading.
https://www.eventzilla.net/e/can-you-pay-to-upgrade-seats-on-american-airlines-2138647967