ATS IS AT THIS WEBSITE (FARE WAS LOCATED AT WWW.TISS.COM, however): http://www.1airtravel.com
I was thinking about this and while it may be a bait and switch, I have found these sites to be pretty reliable. It may be a trip from Frankfurt to US to Taipei, all on United--you can really rack up the miles for cheap. I found a similar thing on Air New Zealand in that it was significantly cheaper from Europe through the US to New Zealand and Australia than if I had booked it directly from US to New Zealand! It seems they are promoting taking the long way home!