I was there from 5/29-6/2. Here's our fastpass+ schedule, the first three each day were scheduled, the rest added
5/29 - mine train, jungle cruise, haunted mansion ( arrived at 9pm) 3 total
5/30- mine train, space mountain, splash mountain, big thunder, pirates, ( hop to Hollywood for star wars characters, then back to mk) haunted mansion, cinderella/rapunzel, sleeping beauty/snow white. 8 total
5/31 star tours, tower of terror, toy story, ( hop to epcot) maelstrom, figment, character spot, nemo, ( back to Hollywood) star tours, great movie ride. 9 total
6/1 everest, dinosaur, ( let safari expire on way to epcot), living with the land, ( rain/ thunder caused is to go back to the hotel for a break) 3 total
6/2 mine train, Anna and elsa, enchanted tales with belle, buzz, leave at 12:30 4 total
Conclusion: 4 th or more fast passes are completely possible. The kiosk were not overly crowded, and were marked on the maps. Waited at most five minutes for a kiosk. Headliners were gone by early morning, so book those ahead of time.