From the introduction to Speaker for the Dead by Orson Scott Card:
[The] difficulty of creating a character increases with each new major character that is added to the tale. Characters, as most writers understand, are truly developed through their relationships with others. If there are only two significant characters, then there is only one relationship to be explored. If there are three characters, however, there are four relationships: Between A and B, between B and C, between C and A, and finally the relationship when all three are together.
Even this does not begin to explain the complexity—for in real life, at least, most people change, at least subtly, when they are with different people...
I have seen this time and time again with my friends, with other family members. Our whole demeanor changes, our mannerisms, our figures of speech, when we move from one context to another. Listen to someone you know when they pick up the telephone. We have special voices for different people; our attitudes, our moods change depending on whom we are with.
So when a storyteller has to create three characters, each different relationship requires that each character in it must be transformed, however subtly, depending on how the relationship is shaping his or her present identity. Thus, in a three-character story, a storyteller who wishes to convince us of the reality of these characters really has to come up with a dozen different personas, four for each of them.