Several comments on doing a triple:
I would define it as three round trips, all within one calendar day. That way, you only need one permit. Any route counts.
There is plenty of water along the way, and you only need to carry enough food for one round trip on each climb. I see no need for support along the way. I'm not sure that receiving support is cheating, but it certainly costs you a bunch of style points. On the other hand, there is no problem having someone handy to make sure you don't collapse and die on the third descent.
Doug and I once had a discussion of the fastest way up. We agreed that it was to solo up the East Buttress and descend the Mountaineers' Route. That assumes you're skilled enough to solo the buttress. I'm not, and never was. The second fastest way up is to solo the East Face. That used to be within my ability, and I once got up in 3:29 from the Portal. 6:00, car to car, including a half-hour break on the summit. I'm not that fast or that brave anymore.
I believe the record of ~2 hours up and ~3 hours round trip used the Mountaineers' Route both ways.
I did my only double two years ago in 19:50, including rest time at the Portal. I never swore not to do it again, but I doubt that I ever will.
RichardP was contemplating a triple at one point. He concluded that he might be able to do three trips without stopping, but the time would be well over 24 hours. I'm pretty sure I couldn't do three trips, and I would be slower than Richard if I did.
I have no doubt that it can be done. After all, Shasta has been done six times in 24 hours (RT from the Sierra Club Hut, not the trailhead).
