Yep, doesn't have to be an Italian, any group that senses a money opportunity would jump on it, but it depends on who actually controls the neighborhood, as they usually has first dibs. Example, in Queens, sometime in the mid 1970s, Lucchese member Tony Russo, and Gambino member Bobby Vernace had a sitdown over a russian running a gambling operation in the basement of his store. A lot of guys were trying to claim that russian, roughly the house took in 8000 to 15000 a month, with a good month netting them 25000 to 30000, which is what brought them to the mobsters attention. The Russian was not hooked up with the Russians, and LCN, made and associates were trying to get in on the action. It came down to Russo and Vernace with Vernace becoming partner with the Russian, in that the crew he was with had a lot of things going on for them in that neighborhood, and thus considered to be running that neighborhood.
Regardless if someone starts to operate and is making some money, someone will notice and then make an offer. Drugs, chop shops, and prostitution being the biggest ones that will bring in them new partners or close up shop.