capo di tutti capi
First there is the Grandfather, who rises above the "street fighter" level, possibly through some contingent event (moving to America; moving from the East Coast to West Coast; moving from NorthEast to SouthWest; opening of a new market etc); this establishes the "Family" as an important player. Grandfather is a nasty piece of works and sets the stage, but only features in walk-on roles or flashbacks. The real story begins with Papa. There are also the "Women" (or reverse the gender roles, it matters not, the meta-theme can be stereotyped), they are often the prime movers, for good or ill, but the story focuses on the sequence of front characters, at least on first read.
Next comes the "Father": he is hustler, smart, street-smart, deceptively tough, ruthless, heart-of-gold (maybe); but fundamentally honourable - he fought his way to the top, and knows how it works - there is a "Code", and you may be tough but some things are out of bounds, even if it leads to setbacks; Papa takes the long view, his ambition is great but bounded, he knows his limits. This is the pinnacle of power for the Family, and now hubris sets in.
The "Son": the Son has it tough - Papa is on top of the world, capo di tutti capi, and he earned it. Papa has a posse of street-smart, intelligent tough assistants who are loyal, and the loyalty was earned; they are men of honour even as the destroy enemies and inflict collateral damage. Their rivals give them grudging respect, even the feds respect them; they control the streets and keep things from going totally out of control.
The Son has it hard - Papa is too smart to just give him it all - and there are Brothers and Cousins who might overshadow the Fortunate Son in an unfair way; sometimes it even seems Papa likes some non-Family Golden Boy even more than Son.
So, the Son has to earn his cred - he does a tour on the streets, not anywhere real bad, just enough to know he slung a gun and could have been in a real fight, if things had been a bit different. Here the Son starts making contacts and building his loyal posse. But his loyalists are mostly toadies, smart toadies, guys looking for an easy ride to the top, sucking up to the boss's Son, and deep inside he knows it - no one can really be trusted, unless they have shown real loyalty, by doing something dirty, violating the Code.
The Son despises the Code - it is for old fogeys, not capo di tutti capi. Rules are for losers.
Papa gives Son some business opportunities, an easy scam or two, maybe a pump'n'dump - so the pump is failing, Papa calls in a favour and someone from an allied Family primes the pump long enough for Son to get out with a success; and a favour owed - that will bite in the long run. Second scam works, softer target, Son is established and sent to run some territory. The posse grows.
Now Papa retires (or does he?); maybe someone else ascends to capo di tutti capi for a while, a player from a rival family; while Son gathers strength. Either way, eventually, the Son makes a move. Now he is capo di tutti capi. He will outdo Papa.
Initially Son plays by the Code; he is smart enough for that. But things are getting nasty behind the scenes. Something sets off a fight. Gloves come off; the opposition is crushed, in a no rules, cinematographic gore fest. No one will challenge the Son.
But, the rules are rules for a reason. Resentment builds. Papa's old posse may have been moved out for some Boni but they start talking, the other Families grumble, nothing overt, but behind the scenes Son's schemes start being subverted. The Feds are getting restless, they like it quiet, no blood on the streets please, and especially no collateral civilian causalties.
The Rule Number One is broken - the Son messes with the Feds; not in a fair fight, a hit, a revenge strike on a small player. Now their own are threatened, and Son gets taken down.
It takes time, it is messy, nobody ever likes this part, too gory, too messy, too many favourite flawed characters go off stage; the rise and hubristic days of glory are so much more fun on the screen.
But, the Greeks were right, hubris costs, and eventually the Son is taken down. Exile, jail, or worst of all, inglorious has-been.
And the cycle repeats; maybe another branch of the Family will ascend; or not. There is always someone else wanting to be capo di tutti capi.