It may be a shame that the second Doctor Strange film wasn't called Doctor Stranger, but Doctor Strange in the Multiverse of Madness is a wonderfully way-out title in its own right: rich with the promise of pulp-fiction excitement and midnight-movie wackiness. Delightfully, the film itself fulfils that promise.

As spectacular as the psychedelic effects were in the first Doctor Strange, which came out more than five years ago, the screenplay stuck closely to what was, at the time, the studio's typical formula, in that it told the origin story of an arrogant white man acquiring his abilities and then defeating a forgettable baddy. The sequel is a different matter – although initially it feels familiar enough.

It begins with Stephen Strange (Benedict Cumberbatch), New York's premier neurosurgeon-turned-Master-of-the-Mystic-Arts, attending the wedding of his old flame, Christine Palmer (Rachel McAdams), and realising that if he hadn't been so pompous, she might have married him instead. But suddenly he has other urgent business to attend to: an enormous one-eyed octopus monster is chasing a girl called America Chavez (Xochitl Gomez) down the streets of Manhattan.

One zany, tentacle-lopping fight scene later, America tells Strange and his fellow sorcerer, Wong (Benedict Wong), that she comes from another universe. In fact, she has the power to hop between multiple universes, which is why the monster was chasing her. Its demonic master wants to steal America's power so that it can rule not just one reality but every reality there is. The only way to foil this demon is to locate the most super-dooper spellbook in existence, and so Strange recruits the one magic-wielder who might be able to help him, Wanda Maximoff (Elizabeth Olsen) from the Avengers. The usual sort of quest gets underway.

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There's plenty of CGI-dependent action to enjoy, but for a while the film doesn't seem like essential viewing for anyone except devoted Marvel fans. Following on as it does from the events of WandaVision and the What If...? television series on Disney+, it's difficult to see why it wasn't just a television series on Disney Plus, too. Slowly but surely, though, the film becomes weirder, sillier, more emotional and more imaginative, with more ridiculous jokes and yet with more macabre shocks. In other words, it becomes apparent that it's directed by Sam Raimi.

Credit should also go to the screenwriter, Michael Waldron, who has knitted together an immensely complicated yet largely comprehensible dimension-jumping plot. He has rightly given McAdams and Wong much more to do than they had in the previous Doctor Strange film, and he has incorporated lots of big surprises that the studio has managed to keep quiet about. But Doctor Strange in the Multiverse of Madness feels like a Raimi project to the core. It could even be the Raimi project. When he made his Spider-Man trilogy starring Tobey Maguire, his adoration of Stan Lee and Steve Ditko's superhero comics shone through, and that geeky love shines brighter than ever here. He was also the director of The Evil Dead trilogy and Drag Me to Hell, of course, and he doesn't hold back on cartoonish horror-comedy scares. The film ends up as a surreal adventure featuring tender-hearted zombies, a green-furred minotaur, a cloak made of the souls of the damned, and a duel fought with musical notes. Raimi hasn't had a new film out since Oz the Great and Powerful in 2013, so maybe he put all of the craziest ideas he'd had in the past decade into this one.

Yes, it's still a Marvel blockbuster that fulfils the requirements of a Marvel blockbuster, and which expects its viewers to have a working knowledge of all of the Marvel blockbusters that went before it. But it's also as gleefully outlandish as any independent cult movie – and there is no way Raimi could have made anything like it without Marvel's footing the bill and laying the groundwork. Some people will dismiss the film as nonsense, and they could have a point. But Doctor Strange in the Multiverse of Madness is a huge amount of fun.

Besides, its appeal isn't wholly reliant on the director's infectious enthusiasm for genre thrills. Beneath the giant walking statues and the alien squids you can find the prickly Strange and the doleful Wanda glimpsing different realities where they are happier, and wondering whether they will ever know such happiness in their own reality. The quieter scenes are acted so poignantly by Cumberbatch and Olsen that you care about the people in the middle of all those digital effects. Raimi and his team have woven a kind of sorcery themselves.