Yorweb,
GB's experience suggests that you might have trouble persuading AsiaMiles to do that on a standard award, but you would be able to do it on a OneWorld Award if you used each of BA and QF for one of the LHR-HKG legs.
In fact the AsiaMiles award booklet here:
http://downloads.cathaypacific.com/m...ardbooklet.pdf
does say exolicitly:
"*One-way awards are available on all airline partners and permit one stopover
except on Finnair, Iberia, LanChile, Japan Airlines and Japan Asia Airways.
*Round-trip ticket awards allow a maximum of two stopovers, two transfers and one open-jaw at either origin, en route or turnaround point, subject to further airline partners’ terms and conditions."
So if GB was trying to redeem a one-way award then he couldn't stopover in HKG and BKK, and in your case on an AsiaMiles award you can route through TPE, but you can only have a stopover of more than 24 hours in two out of HKG, KIX, TPE, HKG.
To do what you want to do I would open jaw at TPE and then get a one-way S-zone award which would just be an additional 10,000 miles in Y.