I believe all three alliances offer such programs. You may have to choose a date, but most will allow you to make changes as long as the required inventory is available. For the oneworld product, you can go to www.oneworld.com
Location: Stuck on this planet - mainly in STR and LAX
It really depends on how many stops you need and how often you are planning to change the dates (or possibly even the routing).
RTWs are very flexible, allow many stops (up to 16 sectors total), book intoi a booking class where you usually can find space, allow to change the routing and are valid for 1 year after the first flight. But they are typically also more expensive. But you need to have dates when you book, which you can easily change later inside the validity period.
Otherwise you could just buy a return trip with the option to make a stop on the way. You ideally would make this on an airline which has a hub where you want to stop (or buy a separate ticket), you also want a fare which allows you to make date changes for a reasonable fee. If you don't want to learn how to find and decipher fare rules a travel agent is likely the best way of finding such fares. You most likely end up with a lower fare, but are less flexible, no additional stops and the cheaper the fare the more difficult to find space on your new date.