Honestly, I was thinking I'd steal a trick from corporate law and make them characters, if rather strange ones.
That's a good starting point.
Let's say we've got three main categories of things that define an Organization:
1. Stats. These are numerical ratings across a few categories. Categories include, but are not limited, to the following:
a. Size is relative to the local standards, and is used for a lot of brute-force effects (the Guild has substantially larger Size than pretty much anyone else economically, and can therefore leverage it to crush foes in trade wars). It also effects how many Subsidiaries an Organization can have.
b. Centralization/Autonomy is a scale. More centralized Organizations get bonuses to top-down effects, but penalties to bottom-up ones. More autonomous Organizations have the opposite.
c. Corruption. More corrupt organizations require additional resources to get stuff done, are easier to bribe, etc.
2. Directives. These are written descriptions of the Organization's primary goals, ideals, and culture. Directives strongly effect what actions and Organization can take: Organizations get bonuses to actions in keeping with their Directives, but penalties when acting against.
3. Traits. These give an account of any miscellaneous, weird resources that can be effectively quantified or used. Things like having wealth far above their ordinary size, having access to some kind of sorcerous backing, or being secretive. Traits allow the organization to perform new types of Actions that would be otherwise impossible, grant bonuses, or in some other way modify the ordinary rules for character interaction or Organization interaction.
Okay, so what can Organizations do? One of the big problems with having as large a scope as you want is that it can easily render–as Shyft brought up–organizations too clunky or abstracted to really function effectively within a game. What I'm going to propose is a tradeoff, one that adds some extra complexity overall, but makes for more engaging interactions within an actual session.
So, here we go:
There are multiple different ways of interacting with an organization.
The first way is to interact with a Representative. This is an individual character: an employee you come across during an encounter, perhaps, or an otherwise nameless NPC who happens to be the face of the Organization in that moment. Representatives have their stats based off of the larger Organization (with some small variation). More corrupt organizations have more corrupt employees, more autonomous organizations have more engaged employees, etc. Generally speaking, you aren't going to be getting much out the Organization directly with this: you can bribe a guy for information or such, but it won't do much to interfere with the Organization proper.
The second way is to interact as a Manager. Managers are placed in charge of some facet of the Organization, up to and including CEO/King/whatever. This effects a few different things. In the first place, Managers have a finite pool of Dice to throw at problems: over a given period of time, they have Dice equal to their Size that they'll need to divide among whatever Actions they're trying to accomplish. Better Managers can get bonuses/dice tricks applied here, but the Organization itself is a limiting factor: no matter how skilled a Manager is at bureaucracy, they can't do something with nothing (unless, of course, they can with a Charm). Depending on the scope of the position, Managers have different Actions available (someone in charge of R&D can only do R&D, someone in charge of a spy network has a lot of latitude, but doesn't control troop movement, etc.). Taking actions at a scale larger than the Size of the Organization is difficult, giving it a big penalty.
Managers can (and are often encouraged to) give Dice (resources) to their Subsidiaries. Subsidiaries are essentially smaller (as in, less Size) Organizations that are part of the bigger one, although they can have some deviation in stats, Traits, and Directives. Dice thus given are multiplied, allowing for more overall projects to be done better with the same resources. Since they're smaller, the won't be able to handle truly big projects, but they'll be more efficient at handling the smaller ones.
More centralized Organizations can have more layers of Subsidiaries but fewer Subsidiaries per level, allowing for far more efficient top-down management. More Autonomous Organizations, on the other hand, can have more Subsidiaries per level but fewer overall, with a larger multiplier effect on dice passed down, resulting roughly the same overall resources but an easier time improvising by lesser Managers.
PCs who are a Manager can try to manage up, convincing a superior to give them more resources, better sub-Managers, etc.
The third way is as an Employee, which should be pretty obvious, manifesting much more as background Dots on your character sheet.
Organizations can take actions in a bunch of different ways, all reasonably narratively abstracted (see Reign for a good reference). Generally speaking, actions are overseen by some member of the Organization, getting a bonus based on their stats but using the Dice assigned by the Manager. Actions also receive a bonus based on the Traits involved.
Thoughts?