Possible but important to fully understand the rules of each award under each program - eg number of stopovers, restrictions etc. You are also unlikely to get much help from the airlines - they will rightly treat it as two separate tickets on separate airlines.

I have successfully booked and paired a AA-issued Circle Explorer (for my father who is QF Plat) with a Qantas oneworld award (for my mother using fathers points), both starting in HKG, but it is not easy to coordinate with flight availability etc... Once you have two PNRs seating is generally easier - although best to call each airline you are travelling on individually with their respective booking refs.