Increasing the number of factions in the story has its advantages. One can much more easily make the story complex, and so long enough for a book. It makes the story world larger.
Still, it can make the arm of coincidence very long indeed.
The Lord of the Rings doesn't have much issue with that. I do not remember wondering about coincidence at the time, partly because the evil things stayed in their lair. Nothing like the Conan the Barbarian story where Conan and the girl of the story, having fled a kingdom on boat, happen on an island where they happen to face the attack of an ape-man, pirates, and a truly stupendously stupid divine curse (why oh why did the curse ever stop for anything? Besides, of course, letting the stone men come back to life and imperil Conan and Olivia) -- that one was noticable even when reading. Still --
They need some reason to happen at once. Perhaps one source of evil magic stirs up others, by sympathy. Perhaps rumors mean that other villains know there are openings that might be exploitable. Perhaps everyone wants the MacGuffin. There's always the ever popular Lead Villain has one (or more) subordinates who have agendas of their own -- or an erstwhile ally decides to get back at the lead villain.
Lots of possibilities-- but they all need development.