Did this myself last February- SQ exec economy is a bargain at 60K miles. Flew EWR-SIN-TPE on SQ, TPE-NRT-JFK on UA. For US Airways awards, you are allowed one stopover; I spent two days in SIN before a week in Taiwan.

One could get creative and route JFK-FRA-SIN-TPE on SQ using your stopover in FRA, spend however long you need at TPE (or whatever other destination), and then fly TPE-NRT-JFK. This way you could get a Europe and Asia stopover? (Has anyone tried this, I assume the JFK-FRA-SIN-TPE is considered transpacific?)