Originally Posted by CarefreeBA

Stopover rules change from origin to origin. Certain markets allow for stopovers both ways for free, some with fees in one direction and some with restrictions such as none in HKG on outbound leg. Using the multi-city tool, you can add a stopover in it for sure; it just depends on if the fare allows it.

Using ITA Matrix or Google Flights, restrict it to only CX flights and you'll be able to work through a few different origin/destinations to see which markets work and don't work. There are a few scattered about but I've not gone to look for any above economy class.