(Note: out of my depth here, but in case this helps...)
While not a direct answer to your question, I'll point out that in the inverse situation - a U.S. investor who wants to buy individual stocks of companies headquartered outside US - you would buy ADRs, which are $-denominated "wrapper" stocks. They can be listed with one or multiple brokerages.
One alternative I'd offer the person in my example would be, "Are you really sure you want to directly buy individual stocks?" One less targeted approach available in the US is to buy ETFs targeted for a given country (or region).
Maybe there's something similar there in Asia that would eliminate the (somewhat) higher fees associated with trading foreign stocks.