You could argue the Sopranos ventured into this type of territory but I think perhaps the most fascinating and unexamined era might be the early/mid '90s.

Think about what was going on:

Lucchese Family: Complete turmoil following the murderous Vic & Gas regime
Colombo Family: Aftermath of their third war
Gambino Family: Downfall of Gotti, dealing with the son trying to be boss, glory days long gone
Bonanno Family: Slowly reclaiming respectability on the street but excluded from commission (and in 10 years time the greatest turncoat betrayal of all time)
Genovese Family: Surrounded by these other idiots.

You could even add: DeMeo Family, dealing with a show being made about them!

Still a lot of guys leftover from the glory days, but also some new guys coming in from a new generation; some of them good, some not so good.

Lots of stories in there, I don't even know which ones you focus on. Maybe you have two brothers in two different families giving you a view of the Colombos trying to rebuild and the Bonannos rising towards the top, while dealing with the other families.