Let's discuss the two words of "criminal enterprise" in separation.
Criminality implies doing something that is prohibited. The degree of prohibition and scope of activities prohibited flows generally from the people in power and what sort of things they need to defend themselves against in the present or near future. A plutocratic system will rarely focus heavily on investment in long-term processes that don't also aid immediate needs and goals. As such, if the vast majority of criminal activity is "whatever goes against the needs of the ruling class", we'll end up having a very fluid system of crime that sees the ebb and flow into and out of legitimacy with the changing of the ruling class.
Enterprise, being an organized operation implies a lot of the same centralized control structures that one sees in a legitimate business. Only the income streams and partnerships happen to be of questionable legality. This, as with the above, assists an organization from rapidly transitioning between "legal" and "illegal" when the winds change.
Examples: Baker's Guild systems that demand specific proportions of wheat in anything that's declared a "bread" will see a black market for rye bread and oat cakes (or inedible garbage fillers) spring up for people who suddenly can't afford to eat even basic bread to survive.
Brickmaker on the ruling council creates a non-compete clause for the region and causes counterfeit bricks to flood the market from outside the region, all imitating (badly) the maker's mark stamped into the legitimate brick.
Both of the example businesses above could rapidly legitimize and compete in an open market the moment the rule is no longer enforced or in effect.
As with all governments, however, some legacy systems may exist that centralize government control over the less-palatable aspects of society. A number of Player Character classes lend themselves well to shadow operations that need subtlety, infiltration, exfiltration, and elimination of targets without being caught.
For those classes, the DM may well choose establish a semi-criminal enterprise that operates within the government, but outside of direct control of the plutocrats, i.e.: an intelligence agency. Whether this is a leftover pursuit of one of the founders (a rogue or shadow monk may be responsible) that grew into an agency, or a necessary evil that got built up over time is up to you; the end result is the same: the ability to operate outside of the bounds of established legal statutes with specific goals in mind: stability of the established community, reduction or elimination of growing threats to the status quo, and development of a controlled external threat to keep everyone inside the city's legitimate structures working together for fear of being toppled from without.
The PCs don't have to be willing participants in such an agency; they can easily be manipulated patsies instead. In fact, part of a campaign may be unraveling political shenanigans that they were initially manipulated into causing unwittingly.