I'm working on booking a trip that would basically be the following itinerary:

ORD-RIX-DUB-MAD-ORD

Getting to RIX (Riga) seems like the biggest challenge. According to AA when using miles you can only have flights on two airlines, so if I were to try to book either ORD-RIX-DUB-ORD or ORD-RIX-DUB, MAD-ORD what do you think is the best way to try to pull this off?