There are two kinds of Faction.
Player Factions - like Vampire. These are used to distinguish between players and give them a source of prebuild and reasonably safe intra-party conflict. I say reasonably safe, because almost always these factions are working together in the setting, like in ToD or the Camarrilla.
Setting Factions - like in the Forgotten Realms normally. These are there to provide storylines, hooks and antagonists or allies to negotiate and fight with. Though players can join the Harpers, say, this isn't the primary purpose of the organisation, which is to be a method of feeding plot to the party. You will want the factions to hate each other, since that way their conflicts can be a source of storylines for the players to interact with.
Thank you for this.
What we need, then, is five:ish forgotten realms factions that can act as player factions. That is, five factions that are at minimum neutral towards each other if not minor allies, but still sufficiently different from each other in their manners, methods and goals to justify having them all along.
The ideal is that the first time, one faction provides an adventure/quest/mission
for the entire party. Then, the second time, it's another faction that starts the next adventure.
The first adventure benefits the first player the most, since it is he or she who advances in the organisation and "unlocks" membership benefits. But that's not of great concern, since the next time it could be my turn - the next time it could be my organisation that hands out the mission, with me as team leader and me basking in the glory (or taking the blame).
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The first thing you probably is thinking of is: the gods and churches. It would indeed be easy to find a cluster of half a dozen gods that work in the same general direction. And you could always consider the class features of clerics and paladins as "faction benefits" that you "unlock" with adventure (read levels).
Problem is, the FR churches are incredibly bland. And, of course, they're not exactly inclusive of random-classed murderhobos.
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What you would want is five factions much like the harpers or the zhentarim, complete with "unlockable" faction benefits, ideas for typical quests, and the like.
But, very much unlike the harpers and the zhentarim, five factions that actually get along with each other naturally. Even for characters that eventually become outright leaders in their respective organizations; meaning that even when it is the players who call the shots, the factions' philosophies can't diverge nearly as much as the harpers and the zhents.
So here's my challenge to y'all. It comes in five parts!
a) Name a significant FR faction that work well with, or share similar goals with,
Emerald Enclave.
b) Name a significant FR faction that work well with, or share similar goals with,
order of the Gauntlet.
c) Name a significant FR faction that work well with, or share similar goals with,
the Harpers.
d) Name a significant FR faction that work well with, or share similar goals with,
Lord's Alliance.
e) Name a significant FR faction that work well with, or share similar goals with,
the Zhentarim.
The idea, of course, is to collect "clusters" of factions, so DMs can offer a choice of compatible or semi-compatible factions, instead of the too-divergent list of five offered by the game as it stands.