What I've read, or some of the articles I've read, indicate that Ricca and Accardo set up the hierarchy with a day-to-day boss with Ricca&Accard retaining final say in the more important decisions. The reason for this was so it would be more difficult for law enforcement to get to R&A. The Boss and underboss (or whatever it's called) were always Italian/Sicilian (may be wrong about underboss) because these were considered the most hardcore old-school mobsters and were less likely to turn. This setup allowed R&A to semi retire and still be involved in The Outfit.

I do recall something about Aiuppa making some "title" changes, but can't recall the specifics. I don't think there would be much disagreement that this setup is no longer in effect. But hey, who knows what is going on with The Outfit ?