The answer is simple. As many as you can comfortably handle. If you can only handle one at a time, do that.

The thing is, don't expect other people to be on the same level as you because people use this system differently.

Also, it is usually rude for someone (or you) to ask on a first meet up "So, how many other people are you talking to while you're talking to me?" I would never ask that, but I would assume i am not the only one. I would also hope that the person i was going out with, wouldn't ask that of me because its a little personal your first time out with someone.