If starting (and finishing) in TPE, I think you may still have a problem. That would make the routing commence with TPE-HKG-DEL-HKG-NRT-HKG and end with JFK-HKG-TPE. I make that six sectors in Asia where you are only permitted four. And you can't purchase additional sectors in your continent-of-origin.
52N . 2. 2 ADDITIONAL FLIGHT SEGMENTS WITHIN EACH
53N . CONTINENT, EXCEPT THE CONTINENT OF ORIGIN MAY
54N . BE PURCHASED. EACH ADDITIONAL FLIGHT SEGMENT
55N . MAY BE PURCHASED AT A CHARGE OF:
Also, I assume you are planning stopovers in DEL and NRT. All connections through HKG will need to be transit only (less than 24 ours).
149N STOPOVERS
150N ----------
151N .
152N . 1. A STOPOVER IS A BREAK OF JOURNEY OVER 24 HOURS.
153N . 2. STOPOVER PERMITTED ANYWHERE.
154N . 3. MAXIMUM 2 STOPOVERS PERMITTED IN THE CONTINENT
155N . OF ORIGIN.
You may need to consider taking the DEL or NRT trip as a seperate ticket??