and if you really want to stop by TPE as well, you can do an open-jaw somewhere e.g. at LHR or NRT instead of a pure stopover. e.g. HKG-CDG/LHR-KIX-TPE-HKG, or HKG-LHR-NRT/KIX-TPE-HKG (of course you need to calculate the miles to make sure it's still zone D instead of E, still CX + one airline allowed for Mixed Carrier Awards, etc)...

but from my experience not too many MPO/AM agents would agree with this, that you can do 2 stopovers (including destination) + 1 open-jaw, but if not, just hang up and call back. e.g. a recent itinerary I have, HKG-PVG/HGH-NRT-TPE-HKG, the first agent I called, said it's definitely not allowed and she's very sure about it etc, then I just said thanks and called back again, knowing well that it is allowed under the rule. then the second agent, who sounded much more experienced, said of course it's allowed and booked it for me immediately. I also told her another agent just told me 2 mins ago this cannot be done, and said it's not the first similar experience I had and asked her to talk to her supervisors to make sure this knowledge got shared properly among all agents.