First thing is definitely best, starting right at Rope Drop, and/or doing morning EMH hrs if you are on property. This also helps to avoid the heat. You can get quite a bit done, focusing on big rides/longest lines like Toy Story Mania at HS, Everest and Safari in AK, TT or Soarin in Epcot(and Frozen ride once it's open), and 7DMT, PP, and the mountains in MK. This is especially true for HS and Epcot with tiered FP, so you can get one done from Tier 1, and FP another for later. As PP pointed out you can get a 4th FP after you use your 3, but as rabidstoat mentioned, by that time FP for major rides are often gone(Fantasmic! at HS is usually available, and it can be used as a 4th one since you don't need it till the evening). Make sure you check the list of which rides are open during EMH at each park if you are going at that time, so you can plan which you want to hit 1st, and which to FP. It's also great if you have two days(especially for MK) to split up the rides and FP.
The other possibility is late at night especially when MK is open late, or has late EMH. Over Thanksgiving week a few yrs. ago, when MK was open till 2-3 am with EMH, once 11:30-12 cam around, DD and I got on all the rides within 10-15 min., riding Splash, PP, Buzz, BTM, Monsters Inc., Pooh, etc. after having done LM, Enchnated Tales, and HM earlier with FP (7DMTwasnot open yet.)