If there's one actual leader, then there is a moderating influence on any group--the rank-and-file membership, intermediate tier leaders, and the top dog (or cat, or fish ...)
If there are multiple leaders and they all agree, all's well. But if there are multiple leaders and they form two groups that move in different directions, then there's no longer a party. There are two parties.
If there are multiple leaders in three groups and they move in three directions, there are then three parties.
Having shown it for n and n + 1, think "proof by induction" any value of n.
From personal experience, when this kind of thing happens at first there's easy intercourse between the groups. People flow back and forth as necessary, working on what's important. In some ways they still act as a party. In others, not so much.
Eventually that intercourse ceases. Boundaries are formed. This can happen due to financial reasons, reasons of relative importance, or because they suddenly line up in a number of ways. We humans like to form communities, and refer to our particular group of humans as "the community" (meaning all others are non-communities, or not really as important). Suddenly, without realizing it, people find that they're in groups. Not because they were forced to, but because they're human and we form groups. "They" are okay as long as they're neutral and we can think of them as "us", but something comes along and they're the enemy.
This transition can take a month; it can take a year; it can take a decade.
If the group is lucky, most of the splinter groups find themselves weak, powerless, and flow back into one group. They re-unite. Sometimes at the cost of great humiliation--they've perhaps all lost power and prestige and take years to regain it, perhaps some of the auxiliary groups are just weakened and chastened.
This kind of split happens innocuously enough. Some subgroup realizes that it doesn't have the power or pull or influence or voice it thinks it's entitled to, and sets up an alternative power center. Maybe it rejoins the collective; maybe it doesn't. But in the meanwhile, while the subgroup enjoys additional power the group as a whole is weakened. Perceptions are often flawed.
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