Would The Outfit have any contact with NY these days?

I know they don't have to business wise, because since they cleaned up the Teamsters and the other national unions, there is no need for them to meet, but don't they have to meet to discuss LCN rules and regulations. Or doesn't the Outfit consider themselves Cosa Nostra? I know from reading books about NY/Jersey/Philly mobsters that they constantly refer to themselves as Cosa Nostra and from reading about Chicago and watching docs I don't get that feeling..