It sounds like you have set yourself a mammoth task with that, and that it will require a whole heap or organisation on your part. Phew, I don't envy you that.
I've got enough problems with alibis myself.
Keep in mind, there is magic in this setting. Mages come in all shapes and sizes, and how able they are in the magical arts. However in The City, it's rare to find a Master level mage, let alone a Archmage or Oracle. (So somewhat useful mages who lack pure power.)
Because I intend it to be a
Grimderp setting*, I think the various crimes committed in the city are easy enough to figure out. Mostly let your mind go to very scary places - that's the kind of megacrimes The Families and The Org get involved in.
As to the setting and how it's carefully stacked together... I would like comments as to how workable this is.
The Princes have the Military, which can stamp out any criminal group that steps out of line, but not all of them. (Explained below.) The Families (and now The Org) are obviously afraid of being stamped out, so they do not do things that would piss off the Princes. In return, the Princes need the Criminal groups to oppress the people and keep them working for cheap. (The City is it's world's cheap goods exporter.)
The criminal famlies don't just oppress the people, but also sell drugs and other illicit ithings to give a outlet for the plebs frustration. (Including selling women for afternoons.) The plebs for their part are so desperate for a distraction from the terribleness of life they continue to use the services offered by the criminal element, and thus keep funding it, even as they ruin their lives with drugs and by not saving up enough to move to real apartments. (For those stuck in shanty slums.)
Keep in mind, the criminals also own much of the agriculture and industry.
There is a bright spot, any Family who does something outside the realm of what the Princes will allow can be smashed and replaced by other Families who quickly take over various parts of their operations. This would be aided by local Gnags who would change allegiance asap and make sure to take whatever they could with them to help their new bosses. Smashing a Family is easy enough, just seize the Leaders of said Family, hire every other Famlies assassins to kill members of the targeted Family, and let assassins who worked for said Family turn independant and hire them to attack the targeted Family. (This is the power the Princes have on the Leading Families - the power to
smash whomever acts 'out of line'.)
My intent is that the city is run in a specific way that if any person moved out of alignment they would suffer, and the entire system would fall. (Like late game Jenga.) Because if anybody tired fixing it, they would pull the piece of lumber from the stack and it might all fall down. That's
Grimderp in my mind.
*Grimderp: Far beyond what mere Grimdark is like. Compare to the current Warhammer 40,000 setting, sixth edition.