Upvote:1
The ITA matrix will support this to some extent, i.e. you can search specific dates ±2 days. For your itinerary with some random dates in February I found a trip for under CHF 1,000.
In these cases it can also be better to split this into two tickets. Book the two long hauls as a single open jaw ticket and the short haul separately. For the same date range KLM has a really nice option for the open jaw for about CHF 600. Unfortunately one ways between Beijing and Tokyo seem pretty expensive so the overall cost may be a wash. However you may end up with a lot more flexibility.
Upvote:1
Back when I did quite a lot of that, I used this method.
You enter a city pair, and you list the fares available. Each fare is associated with a class of travel, but also has lots of rules, including when they are valid, how long in advance you need to book, how long you must stay at the destination and/or if you need to stay over the week-end, and whether stopovers are allowed (and if so, how many, where, under what conditions, on what routing, etc.).
Note that usually the cheaper fares don't allow stopovers, though that may vary a lot from airline to airline. The most common rules are usually spelled out in fare lists, however you'll have to dig into the fare rules for stopovers.
The first letter of the fare tells you the fare class.
Then it's a matter of finding a combination of flights on each segment, where each has availability on the fare class (bucket) you want.
Note that it becomes quickly quite complex if you mix different airlines, which you'll probably have to do if you want a stopover on the outbound flight but not the inbound. You're probably better off going through the same city (large hub for the airline of your choice) both ways. Possibly with a stopover one way and just a stop the other way. It may work out OK for airlines in the same alliance.
If you stop both ways (ideally with a stopover each time), you can try to assemble two round-trips, it may turn out to be cheaper.
Note also that stopovers imply additional costs: beyond the higher fare, there will usually be a bit more taxes.
Good luck!