FWIW, I think Puzo had in a mind a deeper, more multi-layered organizational structure than did (or does) the mafia in reality. I never viewed the various 'Caporegimes' as anything less than multiple 'street bosses' (to use more modern parlance) each with multiple 'captains' (modern again) beneath them.

As Cicci says during the Senate hearings, "Yeah, Senator, the Corleone family had lots of 'buffers'."

That to me suggests more than just Don-->Caporegime-->Buttonman-->Associates as that would equate to just a single real buffer (albeit the Consiglieri would act as an additional buffer in some cases), and that is plainly not Cicci's experience as a lowly buttonman.

Puzo just didn't elaborate on this to any great extent, with the story focusing on the top--where the decisions were made--and the 'sharp end of the sword', where those orders were actually carried out. We don't see so much of what happens in between, but I feel certain Puzo envisaged more depth (and ranks) to the Corleone Family, otherwise so much else just doesn't make sense, such as the entire organization managing with just three 'captains' when real families of the era had in some cases in excess of 20 captains.