I've not booked my FP for our upcoming trip yet, but I plan on splitting us up into groups for some of the parks (there are 7 of us total).
For instance, you might be fine searching for FPs as a whole group for Hollywood Studios and Animal Kingdom (as it seems as if the FP demand is not as high for those parks). For Epcot and Magic Kingdom, where certain rides have a high FP demand (Test Track, Soarin, 7DMT, etc.), you may have better luck splitting up your party into groups of 3 to try and get overlapping times.
I was messing around with FP availability for 30 days out, and noticed that if I split our party up into (2) groups of 2 and (1) group of 3, I could easily get overlapping FP for Test Track. When I searched for FPs for TT as a party of 7, there were none available.
Availability of course will depend on crowd levels for when you are visiting, and whether you have a 60 day advanced booking window or a 30 day advanced window. I only have a 30-day window, so I know I'll have to be a bit creative in how I book the FP.
If you are going to be booking 4th, 5th, etc. FP (day of FP), I would definitely recommend splitting your party up into smaller groups to snag overlapping times for more popular rides.
Good Luck, and have a great trip!