It depends on what kind of "4 park challenge" your setting for yourself, of are you just doing all the parks in one day for fun kinda thing? I believe one version of the challenge is to ride a ride, watch a show/attraction show, meet a character & eat something in each park? Sure...
We usually take the last day of our trip to park hop between all 4 and do our favorite attractions again. This has actually gotten EASIER with the fp+
-Make fp's for DHS
-Rope drop DAK, straight to EE, Safari, watch Lion King, maybe meet a character
-Bus to DHS
-Use fast passes for ToT, BatB,and something else Single rider RnR if wanted, pop through Launch Bay for a character meet
-Boat to Epcot (or to the Boardwalk and walk the rest of the way cause it's faster) do the same style of day. You could also try to get a 4th fast pass here for something that's within the next couple of hours. Usually when we do 4parks we end up skipping Epcot
-Monorail to MK
-Check what's available for fast passes, book something if you can
-Spend the rest of the day til close there.
We stuck with that order as it makes sense transportation wise, you can obviously do it any other way, and the express busses might come in handy too as they'll cut down on transportation/bag check and such.
-Figure out in advance what EXACTLY is a MUST accomplish for you, and figure out what is going to be the most important things to do fp's for! If you dont have that much you want to do in DHS, then save the fp's for the MK mountains
-ROPE DROP IS CRUCIAL
-Bring snacks with you, and maybe even a transportable breakfast to eat on the way to the parks/while waiting for opening