I usually play a maximum of three tables, but have experimented with up to eight. And I've heard players claim to play as many as 32. We can't all do that since we differ in how much information we can potentially process, even with practice. However, I suspect a lot of people could learn to play four to six, or maybe eight.
One key is to realize that you can't play the same game you do at one table. You have less time to make decisions, so you don't want to put yourself in situations where you're likely to have a lot of tough ones. That means playing more of an ABC style.
Related to that, since this probably isn't your A game, you want to play at a level where your B game has a positive EV. Multi-tabling is based on making less money per table, but more money overall by playing more tables.