EXPs can oversell the economy cabin, if at least 24 hours in advance. Unless the passenger is EXP, I'm not sure there is anything you can do, other than do standby at the airport.
From aa.com:
Executive Platinum members and 1 companion can book a full-fare ticket in the Main Cabin on sold-out American Airlines and American Eagle flights when you make your reservation at least 24 hours in advance (except on codeshare flights and flights to/from Venezuela).