I often do an around the world trip in order to hit a 2 or three locations on a business trip. But as others have said, the true RTW fares are often not cost effective for a short (2-3 week), 4 stop trip.
Instead, I will book an open jaw - in this case it would be SFO-HND and ZRH-SFO. it make take a bit of fussing about to find city pairs that produce a good fare. But when it works, it's like magic. For example, I can often get SFO-SIN, LHF-SFO for well under $650 USD economy.
Then I fill in the space in-between - here it would be HND (or NRT, or KIX) to ZRH. And I look for ways to do that effectively.
For example, if you wanted to visit Vietnam (highly recommended), then you might also book an open jaw of TYO-HAN, HAN-ZRH (or MUC).
I usually fly cheap, so I book in economy, but I suspect there could be some bargains in a biz booking as well.
In this way, the asia link does not need to be *Alliance, and gives you more flexibility.