Probably not as many as there are people, but certainly a lot.
Think of a position you could be confident about. Now abstract it. Now, imagine a counter position that is definitely not confident about yours, but is confident in that which you aren't.
Behold, you've uncovered one of the many socionical dichotomies.
It's all a matter of confidence. There are as many types as there are kinds of confident positions in the world. But too, there are also moral questions: if you aren't confident a position is moral, you can bet there is at least the potential for someone to think it is.
In the end, it's all a matter of mathematics. As yet unknown mathematics, to be sure, but try cranking up the Reinin and see what comes up.... +Fe takes many, many guises.