I've seen a lot of PJO/SOA headcannons that Nico and Will are the reincarnations of Achilles and Patroclus. I've even seen fics about Chiron telling Nico and Will about training Patroclus and Achilles.
Hot take: Gay Dads Patrochilles who aggressively ship Solangelo
Nico has known Achilles in canon ever since the whole "swim in the Styx Percy it's totally safe" thing. And we know he spends a lot of time wandering around the safer parts of the Underworld - that's how he found Hazel.
Imagine he's visiting Elysium, catching up with old friends, and he runs into the legends themselves.
Achilles is moderately indifferent about it - at most Nico's that annoying kid who dragged him away from his eternity with Pat to ask about his mom (awkward). But Patroclus takes one look at this depressed boi and says "is anyone going to parent this sad gay child?" "Pat, that's Hades' son." "Not anymore."
And because it's Patroclus, he goes out of his way to get Nico to warm up to them. He makes point to talk to him and give advice and is genuinely glad to see him in a way that Nico never got at camp wasn't used to.
Achilles isn't surprised because Patroclus always had a thing for strays. The girls he rescued during the war, the dogs he snuck snacks to beneath the dinner table, even the younger demigods hanging around Elysium. Still, he pouts whenever bae pays attention to anyone other than him
"-we never got to have children Achilles, this could be our chance-"
Achilles melts
Admittedly Achilles has a lot in common with Nico. Both demigod princes burdened by prophecy, who often felt isolated from others due to their parentage. It's no wonder Pat likes him. And Achilles finds himself relating to this boy more than he expected.
Nico has no idea that he's been adopted. He's just more comfortable around the dead, that's all. That's why Pat is so easy to talk to and Achilles has warmed up to him - he's the King of Ghosts it's definitely some latent son of Hades ability that makes them like him.
They're actually part of what makes him consider leaving camp for the Underworld permanently. He never said it out loud, but the easy acceptance and care they offered was everything he'd been craving.
It makes the choice easy - until Will finds out and flips his shit.
"Will? Who's Will?"
Nico flushes and mutters something about Apollo and war paint and satyr babies before melting into shadows. Achilles turns to Pat with amusement "he takes after you philtatos."
The more they hear about 'Will' the more excited Pat is. He's a healer - he's making Nico eat healthier - he nags him about hiding injuries - he makes Nico smile. Every point seems to check a box in his favor.
Achilles is hesitant - even if Apollo reunited him with his love, he did so by killing him. And if anything hurt Nico, Pat would be devastated and furious ("-like you wouldn't be too Achilles just admit you like him-"). Nico tells him about Will's supersonic whistle and he's reluctantly impressed. Still, he's reluctant to grant blessings.
Achilles insists that Nico needs to bring Will to them to "judge his suitability as a therapon"
Pat smacks his head and reminds him that "-we're dead Achilles, he'd have to die to meet us-"
"-all the better to prove his devotion-"
"Achilles!"
Eventually Will does meet them, either because Nico escorted him to the Underworld or Nico summoned their spirits. Once meeting him, Achilles has a total change of heart. It's hard not to like the kid when he and Patroclus immediately start rambling on enthusiastically about different medical techniques and how Chiron's lessons have changed in the past few thousand years.
Achilles watches fondly as Pat beams at the sun child, who's gesturing wildly while explaining something called 'neurology'. There isn't much use for healing in the Underworld so his love rarely gets to indulge his passion like this.
A glance at Nico shows an equally soft expression on young prince's face and he thinks "alright this could work"
The deceased lovers immediately began ploting some way to bring the two together. Obviously they're limited as they can't leave the Underworld, but Nico visits so often that its easy to slip in some subtle hints - and even outright statements (Achilles' brand of subtlety isn't very subtle) - that they would be good together.
Nico is well aware of what they're up to and is both embarrassed and pleased by the support. This doesn't effect his relationship with Will much except giving him a much needed confidence boost that ended with him, pink faced but steady, asking Will to see the fireworks with him.
Nico's next visit to Elysium was announced as he tripped and stumbled out of the shadows, rushing up to a stunned Achilles to beg him for advice
"-and he said yes and I have no idea what to do-"
"You're asking me? I'm a warrior, not a charmer young prince"
"Yeah, but you still charmed Patroclus somehow so you must have done something-"
Achilles looks frantically at Pat for help, but his love is bent over in hysterics, struggling for air he no longer needs
... happily ever after?
This was longer than I thought it would be. So many people fanboy about Patrochilles, I just love the idea that they fanboy about someone else for once. And Nico needs a pair of supportive gay dads
Edit:
Nico: I can't believe I was adopted by Achilles and his boy toy
Zagreus: First time?
Nico: ... ????
Zagreus: Also, I'm pretty sure Achilles is the boy toy
(Nico also deserves a bamf poly/pan big brother)(and look Achilles has one in storage)(he enjoys cuddling with his various lovers)(long walks through the Fields of Asphodel)(and kicking the ass of the king of Athens)
my-otpkilledme