No. If you start & finish in Asia then the only stopovers in Asia may be at the beginning or end of the itinerary. The rules are reasonably clear on entries to continents - only one, except:
2. Two permitted in Asia when one is a transfer without stopover, or on direct single plane service between the Southwest Pacific and Europe.
Some managed years ago to get that interpreted to mean you could go SWP-N America in transit via Asia for a non-Asia originated ticket, but even that not recently; there's no chance of you doing what you wish to do.