I will gather some non-standard characters in this question. Suppose then the Powerpuff Girls, Team Sonic, Totally Spies, Kanker Sisters (Ed, Edd n Eddy), and so on.
Every time we can identify some external characteristics: The "gothic" personality, the "barbie" personality, and the "neutral/leader" personality. This is, of course, is a quite rough, imprecise analysis. But still, this trope forms a dynamic relationship quite interesting (which seems to work pretty well).
For instance, in the Powerpuff Girls, we have Buttercup and Bubbles; one is quite the opposite of the other: Buttercup has a destructive and impulsive personality, instead Bubbles is the most sensitive of the three, a bare wire of emotion. Then we have Blossom, some sort of a mediating factor between the two other girls.
It seems that these power trios are created when we "break the uno-persona." In other words, it seems that these three personalities can fit into a single character. But these characters (in power trios) seems to have just one single personality.
I would like to know: what are the psychological fundamentals of a power trio trope?