We did Disney last year with a party of 15. 8 of the 15 were children between the ages of 2 and 13. Even with a group that large, we easily used 6-8 fastpasses per day, and we were able to tackle almost all attractions in HS, AK, and Epcot. We were able to tackle all of MK over 2 days. And that was all while dragging around 8 kids that constantly needed to use the bathroom, get a snack, walked slow, and got distracted by everything. That also included stopping for a lot of pictures and character meet and greets. You will most certainly be able to do more than 4 attractions per day. Just use your fastpasses wisely, book the three original ones for first thing in the morning, and then take advantage of being able to book additional passes once the first three have been used. Also, PLAN! Plan how you are going to tackle the park, and watch wait times and take advantage of rides with lower wait times when you can. If you get there at park opening and stay till closing, you will absolutely get more than 4 attractions per day. Also, fastpass lines move quick for the most part, and no one in the standby line really cares.