Won't work I fear
You can do a DONE4 in multiple stages, but it does make planning more difficult. In your case, it's not going to work though. Your continent order is (SWP)-Asia-Europe-(SWP)-Asia-US. If you buy your RTW in BKK, the first SWP won't be a problem, but you're still stuck with the fact that you want to make two Asian stopovers (MNL and TPE) while visiting Europe inbetween. That's not a valid routing in any case. So you're going to have to either rearrange the order of your visits, or you're going to be stuck buying separate tickets.