Yeah, its very possible.
We did the exact same thing on the last day of our two week trip in December 2005. We (DH, DS14, DS12, and me) tried to decide what our favourite attractions were in each park. Once decided, we went back to each one.
We started at Epcot (drove - and it was the first morning that we weren't even there at opening) and hit Soarin' first to get fastpass. We then walked over to Test Track and convinced DS12 to go on it for the first time (we have a wonderful PhotoPass pic of him with a grin from ear to ear!). The clock said 25 minutes wait, but we got in after 5 or 6 minutes (last ones into the pre-show). We hit MouseGear for those last-minute souvies and then walked over to the Land where our Soarin' fastpasses were just open. We waited in the fastpass line for about 10 minutes and lucked out and got the first row again (that was the third time that trip!)
Then we hopped on the bus to MGM. We hit Rock N Rollercoaster with less than 5 minute wait. We had missed Sounds Dangerous when we were there the first time so backtracked and went to that show. We waited outside about 15 minutes for the next one, and while we waited, we bought my younger son his sorcerer's hat that he wanted. We loved Sounds Dangerous. Glad we got to see it. Then we went to see the new Narnia attraction (a long, glorified trailer, but the boys wanted to see it before we left).
Then we hopped a bus to AK where we arrived just in time to see a showing of Festival of the Lion King (waited about 5 minutes outside and then just over 5 after we were seated). We had more character interaction this time (even more than last time) and we did a much better job with our pics this show so it was worth it!). We had time for Kali again but the weather was pretty cool, so we had a late lunch at Flaming BBQ. We wandered over to Dinosaur just in case there wasn't much of a line and there wasn't, so guess who went on Dinosaur again (this time with DS12 keeping his eyes open!!).
We saved the best for last. We hopped on the bus to get to MK.....and still had plenty of time for our favourites. We hopped on the Railroad to Frontierland to get to BTMRR. This was the first ride my DS12 had the courage to ride when we visited earlier in the trip, and this was his third ride. He loved it just as much the third time. If there hadn't been a long line we would have waited for another ride. However, my other son wanted to go on Space again, so back on the Railroad over to Toontown we go, and while we are on the way, my older son is trying to talk my younger son to go on Space for the first time (are you getting the idea my younger son didn't like the big thrill rides?!). Long story short, when we say "Last chance!", he says, "okay, okay, I'll go on it" and we scadoodle over there as quickly as possible before he changes his mind! We waited about 5 minutes and he absolutely LOVED it! My cautious child is now a ride-addict! To finish it off we shot at the aliens on Buzz a couple of times and then left MK for our ADR at the Wilderness Lodge.
The boys did the Whispering Canyon with gusto. They asked for ketchup. My hubby volunteered my 14 year old to hand out the certificates to all the younger kids who did the gallop around the restaurant. We took pictures of us in front of the gorgeous Christmas tree. We got a twilight boat ride and a boat ride in the dark from Wilderness Lodge to MK. We travelled with people coming from Fort Wilderness to
MVMCP who were singing Christmas carols on the boat (and of course we joined in the spirit), and it was just magical.
We watched Holiday Wishes as we hopped on the monorail over to Epcot and we had a monorail car all to ourselves. We just stood there with our noses plastered to the glass watching the show in the sky.
Do we regret doing four parks in one day - was it rushed, or were we too tired? No! Never! Would we do it again? Absolutely! It was by far our best day. Go for it!!

Enjoy!