Oldest son Connor was never in the picture — he seemed an amalgam of the worst bits of Michael Bloomberg and Steve Forbes. That left second son Kendall, with his crumbled marriage, fragile ego and persistent drug issues … third son Roman, a foul-mouthed sprite lacking moral compass and boundaries … and lone daughter Siobhan, who rightly considered herself the brains of a family that didn’t put much stake in women or their brains.

The slow cracking of Greg the Egg

The battle lines were drawn. But then Logan recovered and, far from passing along the keys to his kingdom, forced his children to prove themselves worthy of them. It was as if Lear paused in the middle of Act I, Scene 1, and said, “Holy hell, what was I thinking?” and then goaded his three heirs into never-resolving side negotiations that left them questioning who they were. For this Lear, there was no raging against a tempest on a heath. He was the tempest.

And so a show that seemed to be following one Literary arc began to wander down any number of others. Indeed, with each new season of “Succession,” which wraps its glorious run on Sunday, it’s become clearer that no literary skeleton key will unlock all its meanings. The show wears its influences not as shackles but as layers.

All the same, don’t we get a gold star for trying? I spare now a mournful thought for the classicists who seized on each antique allusion — Rhea, Tacitus, Coriolanus — to build their cloud castles of theory. Surely, Logan was meant to be Cronus, king of the Titans, swallowing each of his children whole at their birth — or else he was Cyclops. Kendall was greeted in one episode as “Oedipus Roy,” but maybe that was a better fit for Roman, whose feelings for the decidedly maternal general counsel Gerri extended to texting her pics of his penis. The show, in effect, gave us one rabbit hole after another and said, “Dive.” Did the Tolkienesque surname of Shiv’s now-estranged husband, Tom Wambsgans, suggest he had the One Ring to Rule Them All? Was Cousin Greg meant to evoke Balzac’s Cousin Bette, a poor relation swearing vengeance on a richer family?

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Or were we to take our library cards and do that thing that Logan was always suggesting people do? Names aren’t destiny, after all. Shiv, it’s true, has her razor-sharp edges, and her balcony smackdown with Tom boasted all the marital blood sport we associate with Edward Albee and August Strindberg. Yet there was something almost Hamlet-like about her inability to commit to a single man or cause, while her disgust over the Roy patriarchy recalled the deposed queen of “The Lion in Winter,” who greets her scheming sons with, “My, what a greedy little trinity you are: king, king, king.”

In the end, though, perhaps the show’s most enduring literary legacy will be the one we are quickest to laugh off: its astonishing art of invective.

Anybody can insult anybody, but it takes a certain kind of genius to hone insult into poetry, and nowhere has that genius been better cultivated than in Great Britain — a lineage that includes the late Martin Amis on “Don Quixote” (“an indefinite visit from your most impossible senior relative”), Virginia Woolf on E.M. Forster (“limp and damp and milder than the breath of a cow”), Evelyn Waugh on his 6-year-old son (“I have tried him drunk & I have tried him sober”) and that master of all registers Shakespeare (“I do desire we may be better strangers”).

Small wonder that the creator and many of the writers of “Succession” are British. But what gives their work its special zest is how deftly they harness both Anglo-Saxon obscenity and American idiom to create a distinctly mid-Atlantic vituperation. Logan to his chief financial officer: “Karl, if your hands are clean, it’s only because your whorehouse also does manicures.” Shiv, catching a whiff of her little brother’s fragrance: “Oh, what is that? Date Rape by Calvin Klein?” Logan’s disaffected brother, upon learning there will be a Logan Roy School of Journalism: “What’s next? The Jack the Ripper Women’s Health Clinic?”

A common viewer complaint against the Roys and their retinue is that they’re all so awful, and it is perhaps their only saving grace that they take such pride in anatomizing each other’s awfulness. Literature has bequeathed us a deep bench of entertaining rogues, and has made it easier for us to enjoy them by opposing them to some plucky figure plumping, however ineffectually, for goodness. Lillian Hellman’s “The Little Foxes” showcases a murderous capitalist so delicious that actresses queue up to portray her. But Hellman’s dogged moralism insists on offsetting her with “nice” people — a weakling husband, a pure-hearted daughter — who, by no coincidence, are the least interesting characters in the play because they exist purely to balance its scales.

“Succession” scorns such accounting. “Life isn’t nice,” Kendall declares, “it’s contingent.” And that contingency is what ultimately forces all the show’s characters to become (Lear again) “the thing itself.” What can decency do but quail? The show’s most telling arc belongs to Willa, a former sex worker with dreams, soon scotched, of becoming a playwright like Hellman. Last season, she wept bitter tears when Connor proposed marriage; a year later, she was happily plotting a new life as an ambassador’s wife. “Succession” is about what it’s like to live in a world without sentimentality or piety or assurances. The world we made, Cronus help us all.

Louis Bayard is the author of “The Pale Blue Eye” and “Jackie & Me.”