Most of SE Asia is available to you as a stopover location as well. The UA website will mostly show you their gateways as stopover points but you can assemble an award "chunk-by-chunk" doing, for example, a search for WAS-BKK then BKK-SYD at some later point in time.

For an even more advanced version you can try putting an open-jaw in at the stopover (e.g. WAS-BKK; SIN-SYD; SYD-BKK). Also keep in mind that SQ-operated flights no longer show on the UA website and that you'll likely need to call in to book the award once you find all the flights.

Also, with the new rates partner awards may be more expensive than all UA metal but the extra stop(s) may be worth it.