Question: Can I combine a cash itinerary with an award itinerary?

I've booked a 1-week trip through Air Canada next year using points.

Outbound: San Francisco (SFO) to Seoul, South Korea (ICN) flying Asiana business class
Inbound: Seoul, South Korea (ICN) to Taipei/Layover (TPE) to San Francisco (SFO) flying Asiana and EVA Air business class

I'm actually based out of Dallas (DFW), so I'll need to book a positioning flight to San Francisco (SFO) and back which I'll pay for in cash in economy. I'll look for something through Star Alliance if this is possible, if not, I'll just book the cheapest positioning flight there and back.