Unlimited stopovers theoretically, but the SQ rules are pretty restrictive so you're probably limited to 4 or 5 max, as long as you keep going in the same direction. The big restriction is that you can't visit the same city twice (even SIN) even for a connection... so once you've stopped or connected in SIN, you can't go back. I believe SQ has a BKK-NRT NS so you could do JFK-FRA-BKK (connecting in SIN)-NRT-LAX.

SQ's local US sales offices are the best to test and help you on a potential itinerary. DO NOT call the 800 number... goes to India and that call center is pretty much useless for this type of fare, even if you can understand them.