International Flights & Local Travel

I'm applying for a F multi-entry China Visa. For business purposes, I need to travel from the US to Seoul, then Shanghai, and last stop is Hong Kong. Can I book my international travel with one carrier (US to Seoul, Hong Kong to US) and the more local travel (ICN to PVG to HKG) with a separate carrier? In other words, 2 separate flight itineraries? Or would this be a customs violation.