The next series definitely in the Percy Jackson universe. The Red Pyramid has a hint that it may be in the same universe, but nothing more than a hint. I noted when I first read it that it would make the metaphysics of that universe rather more complicated than the Percy Jackson series made it look. The Lost Hero makes it definite. I think that it can be read alone but it works a lot better after the Percy Jackson series. Also, the Percy Jackson worked up from somewhat milder adventures to one of deep significance. This book takes off where it left off, just as dangerous and significant. The troubles in this book are clearly more than can fit in it.
Anyway -- Jason finds himself on a bus with a whole crew of delinquents, not remembering anything of his past life, with Piper and Leo insisting that he knows them and they are friends -- and when they get out at the Grand Canyon, he takes on Coach Hedge, who, it turns out, knows he's not supposed to be there.
That's when the storm spirits attack.
Much fighting later, all the children are fine -- at least after Jason saves Piper by flying -- but Coach Hedge is gone, and the chariot arrives, with Annabeth. She's peeved, because she had an prophecy that told her she could find Percy, who has vanished, here. Instead, she found three new demigods. And because Jason lost his shoe, she knows they are the right ones.
Well, back to Camp Half-Blood. We start to flip POV -- it's all third person, with Jason, Piper, and Leo all have POV chapters -- and learn that Leo can summon fire, which is very rare among Hephaestus's kids, and not a good sign at all, and has meant terrible things in his past. And Piper is haunted by dreams that threaten her father if she does not betray her friends -- plus her memories of the last months with Jason appear to have been, well, fabricated.
Chiron, at his first glance at Jason, tells him that he should be dead. And Jason is odd in many respects. He speaks Latin, not Ancient Greek. He has a sword that is Imperial gold, not celestial bronze. He has a tattoo of some significance. And he thinks he's Jupiter's son. Which is where the metaphysical weirdness sets in. With some help from Piper. Her father's Cherokee, and Cherokee tales, if not characters, pop up. Her father observes that the sky has room for both Heracles and hedgehogs, but if these tales start to come true, it's going to be interesting.
The threesome set out on their quest to solve the current new problem. On the way, they encounter Olympian Weather Channel, a stark raving mad god, ground that sticks to their feet, an ancient Greek who didn't learn his lesson after all, dreams from a pirate broadcast, clothes that Aphrodite dresses them up in, a somewhat damaged bronze dragon (it's on the cover, and the guy at the register was wondering why a robot dragon, and I guessed that Hephaestus or one of his kids did it -- and I hit it -- go me!), a crayon drawing Leo made when five years old, and monsters that do not return to Tartarus when killed, which is rather annoying.
Spoilerish comment (highlight to see): I wonder if Tristan MacLean is some kind of Oracle type, like Percy's mother, only he couldn't cope with the information. Either that or Gaea really can hold back the Mist so that mortals can remember. Except that Percy's stepfather seems able to realize that Percy is a demigod, so possibly it's just that Mist can be sloppy about the edges.