Back when I multi-tabled FR (first of the year) I routinely managed 9-12 tables easily, and as many as 16 for shorter periods. By "managed" I mean, kept up with the action. Unfortunately it proved to be unprofitable (although RB helped soften the blow a lot due to increased volume). In hindsight I've realized the most likely cause of my losses, and it was brought home the first couple of times I tried to play Rush.
When playing either Rush or 9+ tables, the action was very fast, and I would naturally get wound up in response. Kind of like an adrenaline rush, my heartrate increased and my attention span decreased, and I fell into a high-paced rhythm. After awhile I would stop thinking as clearly, not because I have too many tables, but because I'm anticipating the next hand on the next table, instead of taking the time I do have to focus on the immediate hand. It wasn't that I didn't *have* the time, but I failed to *take* the time. I would get addicted to the pace and would push myself to move faster, making snap decisions even when I didn't have to. The more I played the faster I played, and when I would stop after a long session of Rush or multi-tabling, I'd still be hyper for a few minutes after until I gradually wound down. If you've ever done any distance running, it's similar to the feeling you have after running a 10K or longer and then trying to stop too suddenly -- the body is resistant to the dramatic slowdown and wants to keep up the pace.
Since then I've learned to 2-3 table Rush and make an effort to actually relax in spite of the pace. I stopped rushing my decisions just to get to the next hand. My Rush results were much better, and so I have no doubt that when I return to multi-tabling FR, those lessons learned will help me there as well.
For the moment I'm back on a SnG/MTT phase where I only play 4 tables (typically) at most. For me, tournaments are harder to multi-table just because of the larger number of variables between each table (blinds, stacks, speed, bubble dynamics, short-handed dynamics, etc.) if you aren't careful to play the same structure and start them all at exactly the same time. I can't count the number of mistakes I've made by playing one of my tournament tables wrong simply due to not remembering at what point I was at in that specific tourney.
So, in summary, I believe there are at least two steps to learning to multi-table profitably and effectively, and both sound contradictory to each other. One is in learning to speed up your thinking and reflexes in order to keep up with the action, while the other is to slow down in spite of the fast action and take as much time as you have to make a proper decision. In other words, don't play any faster than you absolutely have to to keep up. It may sound easy, but for me the latter was harder than the former.