The key is not the separate PNRs, but the baggage interline agreements. You will need to check with the airlines involved to see if they will interline your bags. If you have long layovers, you may also want to ask how that will affect you. I once had an airline refuse to receive my interlined bags because my layover, while less than 24 hours, was over a calendar day. This was despite the fact that there existed an interline baggage agreement. That was not fun.