So this is what they do for fun in CHC?
You can purchase 2 extra segments per continent other than the continent of origin which changes the result. AA has some multi-hop flights that touch other countries in the Carribean but they are seasonal (SXM-SJU-LAX pops to mind); I'm sure there are a dozen other Carribean flights which would touch 2 islands/countries. For Europe all I know about is LA SCL-MAD-FRA is a single flight number but that can't be used on a xONE3 fare (no way to cross the pacific without touching NA).