Bear in mind that the stopover has to 'enroute' and not as a sidetrip.
Say you're travelling from LAX-BKK on CX. Your stopover is permitted only at HKG and you cannot detour to somewhere else like say TPE.
Sometimes asiamiles can be very particular as to where your stopover is permitted. Case in point from personal experience.. LAX-x/HKG-BKK-SIN. Oneway award. Final destination is SIN. I wanted a stopover at BKK. Asiamiles wouldn't allow it and insisted that I can only stopover in HKG.
As there is nothing set in the rules.. I had to abide by theirs.