American Airlines is offering premium economy on a growing number of domestic flights. This move will affect a relatively small number of routes: The changes will apply to domestic flights that have a premium economy cabin. Plus, AAdvantage elite members flying on the carrier's new Airbus A321XLRs won't get into AA's new Flagship Suites quite as easily on domestic flights. Premium economy, not business-classBeginning Aug. 25, you economy passengers on will only be eligible for upgrades to premium economy — not business-class. These are the planes that have Flagship First, business class and economy cabins (but not premium economy).