It depends on your ticketing class. Each ticket depending on your booking class and issuing countries has totally different restrictions.

e.g. a Q subclass ticket (dirt cheap one) doing TPE-HKG can be rebooked w/o penalty on other flights but not a ex-HKG Q ticket for HKG-TPE

Best is check the ticket booking class and give CX a call to confirm the rebooking restrictions, but as your ticket rules say (which I suspect a multi-stop / open jaw ticket) the most restrictive rules applies. I think you can check online for your exact ticket rules under "manage my booking" but not so sure (I don't have an active booking right now ... )