Theoretically, the FP+ Kiosk's work like the old FP machines. Instead of going to individual attractions for a FP, you hit up a Kiosk to check availability and book a reservation. So, after your three reserved FP+, you can obtain a 4th, 5th, 6th, etc., etc. Of course, dependent on a lot of factors, some people have met with success obtaining additional FPs while others have not.
Some people like to schedule their three early, to increase their chances of finding availability for additional FPs. That seems to work well in the MK, where there are a lot of attractions and no tiering. Not so much at DHS and Epcot. FPs aren't all that necessary in AK if you rope drop.
We are fans of rope drop at all the parks, hopping to a different park later in the day, FP+ in hand. However, that strategy isn't best for obtaining additional FPs.