like I said above it's funniest if Annabeth somehow still gets sent on a suicide quest. so Athena's having a breakdown for reasons separate from the main plot, I don't think the specifics matter right now bc it's midnight, but let's say she's mad that her daughter is moping (over her missing boyfriend mind you) and starts yelling about how Annabeth never brings any honor to her mother's name, she only gets in the news when Percy's in trouble, dumb shit like that. and she tells Annabeth to not come home until she does something noteworthy, and instead of being reasonable and 1) just moving in with her dad or 2) starting a charity like rich people do when they want good press, Annabeth's like well fine I'm gonna do the hardest possible thing I can imagine and track down a statue of the goddess you're named after that's famously been missing for centuries. fuck you. then your name will FOREVER be associated with me bitch.
So she takes Piper, Jason and Leo with her- Jason is a big history buff, he's a good help with research, Leo is good at squeezing into weird and tight places, Piper has a lot of travel connections through her dad and is definitely able to flirt her way into getting access to dig sites. They PLAN to also take Nico, cause he's a little freak and is good at sneaking around, but when they get to the school in California they find out not only that he's been kidnapped by his evil great grandmother, but PERCY IS THERE!!
Percy's memories don't come back as fast as they did in SoN, but he does remember Annabeth so he's like immediately on board with this stupid rogue archeology trip. Hazel decides to come along bc they already had reason to believe Evil Great Grandma is in the Mediterranean, and she's hoping they can try and track down Nico while they're there. Frank tags along bc his fucking house just exploded and he has nothing better to do quite honestly.
Many, many hijinks later they get info that Gaea has an extensive collection of stolen ancient art and she Knows they're looking for the Athena Parthenos and she offers Nico's freedom in exchange for the location they think it's buried. Percy is like "bet" and then just lies about the fucking location after they get Nico back so she's on like the other side of the country once they get to the parking lot in Rome that Annabeth has narrowed down as the most likely spot. Piper manages to get some permits and Leo's on the excavator while the others just have shovels and are sifting through rubble.
They DO find the statue, obviously- but since they're also a bunch of teenagers that have no idea what they're doing, all the digging triggers a huge fucking sink hole. Percy and Annabeth fall in and everyone assumes they're dead.
Meanwhile Percy and Annabeth are having like, "journey to the center of the earth" bullshit happening to them, and after about a month manage to make it back to the surface, grab a phone from the first kind samaritan they find and call in to CNN or BBC World or whatever and are like "hey yeah we're alive. listen there's a huge fucking super volcano underneath most of Italy from what we could tell, and it really doesn't seem like it's gonna be dormant forever. heads up? yeah we entered in Rome and we're now in fuckign Sicily somehow??? huge underground and underwater volcanic network guys and it seemed pretty Awake"
and then, because they just gave away their location on live international TV, they are PROMPTLY kidnapped by Gaea's people and taken to Greece.
Meanwhile, their friends and family are all on a plane to Athens to honor their memory while officially restoring the Athena Parthenos to her rightful place. They're in the air while Percy and Annabeth are calling into the news, so they completely still think they're dead until they get to the Parthenon and find those bitches Tied To A Ritualistic Altar.
Huge brawl between the assorted Olympian family (and extended friends) and Gaea and her henchmen. Half the Parthenon gets destroyed. International scandal.
However, between finding the statue/surviving underground/successfully warning people in time for scientists to come up with some bullshit to stop the volcano, therefore preventing what probably would've been an extinction level event- Annabeth and Percy managed to get just enough good press that Thalia got to stay happily comatose.