This article is from the Dissociation FAQ, by Discord (firstname.lastname@example.org) with numerous contributions by others.
Err...infinite numbers, I suppose.
Each alter, from the birth person on, can split again and again
into 2 or 3 or 5 or more parts, and so on and so forth. Further
stress usually causes further splits.
Some multiples seem to create alters, rather than split them off. That
is, an alter will appear who really has little in common with any of the
existing alters, and doesn't seem to have split off from them.
Sometimes the alters merge into a new (or into an old) alter, lessening
the number, either because they need to form a alter that combines the
qualities of others, or because the degree of separateness is no longer
needed, or for no reason at all.
The highest number of alters within a system we are aware of is something
around 700, and we have heard claims of multiple systems with alters in the
thousands. The lowest is, as you might expect, 2.
Many multiples fall in the double-digit range, that is, 10 to 99. It seems
it is rare to have less than 5 alters. There are a number of multiples that
have a count in the lower hundreds (100, 200, maybe 300), but it also seems
to be rare to have more than that.