Well I personally would like to see more angles than just the stereotypical one, especially if you were squashing such groups together for plot purposes. The nature of such broad and varied groups is that, if you have to intersect them, the range in what you can do with them becomes narrower for every Faction you involve. Right?
Let's look at the Revolutionary League. If you want to focus on them cooperating with other groups, there are ways that can be done. They're not just violent extremists. The Revolutionary League are countless, individual groups of cells that operate completely independently, such that no one group can be tied to the whole and used to build up the Faction or break it down.
The Revolutionary League has sub objectives and things they want to achieve that are not just blowing stuff up and overthrowing other Factions. For example, they have a large presence in the Inner Planes, especially the Quasi-elemental Plane of Lightning, where they battle against Yugoloths tampering with the fundamental building blocks of reality. They also have many, many influential individuals dedicated to mastering the portals of the Cage, and freeing them from the hands of private groups and Factions.
The Free League are also more than just market place watchers. They have everything from criminal syndicates and assassination houses to the palaces of the Golden Lords of Sigil. They number from the most clueless berk who just stumbled into Sigil to the ruler of the largest castle in Sigil and everything in-between. They have artists, philosophers who push expression and self agency, and even the Guilds of Sigil which run monopolies on the trades which the City of Doors depend on.
The Fated have a very specific reputation as debt collectors and greedy berks. But like every Faction there's a wide array of influence and activity there. Their leaders are developing castles and standing armies around the Planes and in Sigil preparing for war. They have a long history going back and forth from being against and being under the thumb of the dark forces of Baator. Yet their philosophy has formed from the honourable calls of Ysgard, and that - not Sigil - is the centre of their power, where most Fated call home. Their Might Makes Right philosophy isn't just breaking legs and collecting taxes, even if their relatively recent stint of confiscating Bibgy's Arcane University and turning it into their Faction headquarters has put a big focus on that as a method of becoming more powerful.
I mean, I know I'm not a DM here or anything. I guess what I'm just trying to say is that if I wanted to see a plot that involved these three groups having to work together, I wouldn't want it to just be more market place drama. They're not just
Marketeers. There's areas where these groups all cross over - sword and castle high fantasy out in the idyllic but violent wilds of Ysgard? Fighting the machinations of the Fiends in the Inner Planes, where they're trying to cut out the middle man and rewrite reality so that they can snatch freedom and good from all? Vying between the Golden Lords of Sigil and their massive estates, and rivalling corporate enterprises?
Anyway those are just my thoughts. I wasn't going to post but then I thought, well, maybe someone would think this was a helpful bit of insight and opinion.
Let's just have fun.
:)