Sure can
You are allowed up to four flight segments in Asia, and because it is the continent of origin - only two stopovers

If you stop in NRT and return home on a separate ticket, then NRT counts as one of the two allowed stopovers - so one stopover left, but four flight segments still available

Something like this might be attractive:
...NRT-xBKK-oCMB-xSIN-HKG, or
...NRT-oDEL-xBKK-xNRT-PVG
(this second to show that the itinerary can end in China - this is specifically allowed in the rules)

(x = transit, meaning strictly less than 24:00hrs from scheduled arrival to scheduled departure
o = stopover)


Note also that AA flies from the USA to PEK and PVG - so either of those could be your first Asian stopover