Yes to work out how the Corse work is to basically look at Corsician Gangs, the French Connection and Mafia's have worked in the past, and still do now.
For the most part they will try to make sure their operations are insight of their customers, but not those that are looking to bring down that operation. They will also go at great lenghs to bribe Police, Armed Force's, Lawyers, Press, Mayor's, basically anyone with any kind of power that is usefull to them.
But when their is those that come knocking wanting to bring down their operations it usually ends in bloodshed of one form or another. (Assassination, intimidation, assault, kidnap, bomb, torch, smash, any kind of medium or high crime)
With other gangs, traditionally Mafia styled organisations tend to avoid/deal with them where it benifits them. Though generally avoid unless they are wanting to make a lucrative deal with each other. Once another gang starts stepping on their turf it usually turns to violence. (Stepping on ones turf by meaning is of, taking a cut out of profits out of a shop that you was collecting money from. All the way to killing a couple low level members or damage to ones own operations.)
Edit: @Jansen: You seem to me to not to have a keen knowledge of Corsician gangs, for which they are just a Mafia. The term Corse and Corsician was made by the Americians. And I am a Mafia film and historian nut. (Not so on individual gangsters, but on organisation and how they approach things.)