I've participated in 5 separate gaming groups concurrently for several months and enjoyed it very much. But, to DM for more than one game a week would really be a bit much IMO.
Some groups really demand more time than others. I had one group that was happy to game for 3-4 hours once a week, and another that wanted one 8-12 hr session each week. Believe it or not, it was the shorter session that was much more satisfying to me, mostly because the players didn't dally with details or stall the game with interruptions. Personally, I need to get my game on, and then move on to my next hobby, or work, or whatever.
Even with what I think is a very powerful and plentiful "grab bag" of DM components at the ready, with too many different games running at the same time, it can become hectic at times to keep things straight in one's head. If that ever happens to you, you're probably gaming too much.
Anybody who can gather a regular group more than once a week is at an advantage IMO, but three times a week, and I have to wonder if they shouldn't try something else as a group activity just for some healthy variety.
Would I run, as a DM, three sessions a week? I don't think I could do it for any consistent length of time. And moreso, I think it has to be a kind of experiement to try something like that in the first place, while everybody finds out how comfortable they are with it. If after a couple weeks of it, everybody is okay with it, then sure, why not?