Mafia would not be permitted to "Rub elbows" with the dynasties you mentioned. But, it's possible--probably in some cases--that their enterprises had contact with and did business with mobsters and mob-controlled organizations, such as Mafia-controlled unions, construction companies, business associations or "consultants." They do rub elbows in Europe, Asia and Latin America.
Would you say that some old mafia leaders wanted to become as powerful and rich as some of these people though? And were any of them on the track to be on their level? One I can possibly think of is Moe Dalitz.
