THIS is a goal I am setting to do some day. Basically it's climbing 29,029 ft which is how tall Mt Everest is. They rent a mountain...you hike UP the mountain. Ride a Gondola back down....then hike back UP the mountain...a total of 8 times.
It has INCREDIBLE support. I'd likely do a very lightweight pack as you won't hardly have to carry anything at all...but it's also VERY expensive as it includes your room. $6795 dollars for the Salt Lake City one.
I WILL do this some day. Does this sound like fun to you? It does me! :-)