nores to myself
Agile doesn't solve this problem. The situation is almost certainly that upper management is unwilling to either properly staff the projects or adjust expectations of delivery dates. The solution is to try to educate them. They will not listen. Soon enough, every project is the number one priority, with an emphasis on a given project that shifts daily/weekly at the whim of the CXO. Eventually, you and your coworkers will jump off that sinking ship.