Your question is pretty close-ended, so I will do my best for you.
The simple answer is ''no." And to be honest with you, it's not exactly an Italian-American phenom either. Just to give you an example; you named Cosa Nostra in your question and though these organized crime syndicates initially tried to maintain a secret society type of culture, we still have a pretty good idea of when and how they rose up. Cosa Nostra which literally translates to 'our thing' is a Sicilian based gang that began to rise up in very early 19th century Southern Italy during the transfer of feudal baronies to privatized ownership - this is the start of capitalism in Italy. During this time which is popular because of the Napoleonic Wars, Northern Italy was going through industrialization and the South was left behind in the sense that their industries and trades were becoming less and less needed. With less work and rising food prices and the recent transfer of government made the region of South Italy semi-anarchist. Crime was rampant and the local law enforcement couldn't handle it so young men were recruited and employed in a form of brigands, but they became more and more like bandits themselves. As you would imagine, if someone came up to you acting like a cop but isn't one, you're not going to be very compliant, and since these young men were most likely already prior criminals they were willing to do the dirty to get the job done. The thing is, you wanted some of these rough guys and ex-criminals, because they were willing to do it - it almost created a catch-22. Eventually these people became employed by others for protection, almost like a feudal company ironically enough, and the mafia or at least pre-mafia got their start.
It's quite interesting because if you fast forward some time in New York, a very popular (to be) gangster known as Salvatore "Lucky" Luciano started his little gang when he was young by receiving payment from Jewish kids that had money in return for protecting them against other Italians that would have bullied and ultimately tried to shake down these wealthier kids.
In any case, with Southern Italy doing so poorly economically speaking, it sparked a wave of migrations out of Italy into the lands of opportunities - many people came to the USA but also Canada, Argentina, Australia, New Zealand and there are even Italian communities in other Latin countries as well as Brazil though those were usually not their target like my former examples were.
In the end though, a lot of these families that left Southern Italy left with nothing. They came to places like the USA needing to fight and claw their way upwards and since many of their kids (even young kids) were already essentially criminals in the homeland, they resorted to what they knew best - crime. They would start small with things like personal protection or professional rough men and it would lead to something more like cigarette smuggling or selling liquor during prohibition, murder of course and as this continued to snowball and they became more powerful, extortion, money laundering, political corruption, conspiracy....you get the point. But above all of this was a lot of the people that escaped. La Cosa Nostra was Sicilian, and Camorra was Neopolitan, there were also gangs from Calabria, Puglia, Corsica, etc. Think of them as tribes and once they rub up against each other they feud and do dirty things like backstabbing each other. If I was a leader of an organized crime syndicate, and you were as well, and we made an agreement that meant peace but one of my men killed one of yours, then you would demand retribution. A payment of blood....but that blood you want is my nephew's. One option was to run away to some of these Italian populated areas around the world, and these gangsters didn't just change, they brought their ideas and mentality and way of doing "business" with them and exploited the kids of some of these struggling families with the simple notion of tribalism. Maybe you're Italian and I'm Italian, better yet, you're from Calabria and so am I! Come work for me at my business!
Since this was an Italian 'thing' for the lack of a better word, Italian communities around the globe who came from a rough background and potentially didn't know better, they resorted to what they knew. An old Italian saying went something like: "never underestimate the ability for a hungry dog to find something" it makes little sense in English but the idea of the saying is almost like where there is a will there is a way, and like a hungry dog these gangsters had the ability to "sniff" out corruption or loopholes in whatever part of the world they were in.
Hope this helps.
Cosa Nostra by John Dickie
Blood Brotherhoods by John Dickie
American Mafia by Thomas Repetto
The First Family by Mike Dash
Hi there - we're not removing this thread, but wanted to get in ahead of the inevitable comments remarking on the contradiction in your header. Are you asking if non-Italian immigrants had something similar to the Mafia, or if different groups of Italian immigrants had their own branches?