Hatstalls are rare. In Harry’s generation, only Neville, Hermione, and Harry himself even came close. Albus Severus Potter was probably a hatstall, as were Minerva McGonnagall and Peter Pettigrew. Many Harry Potter fans see themselves as a combination of more than one house, and I would argue that most of the characters are as well, but the Sorting Hat rarely has such trouble picking out the house where a character will fit best, and it is almost never wrong.
Has there ever been a four-way hatstall? It seems doubtful. And yet, I can think of one character who just might fit the bill: Albus Dumbledore.
Dumbledore was a Gryffindor, and as far as we know, that’s all he was. A straightforward, moment-the-hat-touched-his-head Gryffindor. In fact, given that Pottermore calls McGonnagall and Pettigrew “the only hatstalls personally known to Harry Potter”, he probably wasn’t a hatstall, at least not in the technical sense of the hat taking 5+ minutes to decide. That doesn’t mean he can’t have been close, though, or that he doesn’t have strong traits of the other houses.
Gryffindor is obvious. Dumbledore founded the Order of the Phoenix, stood up to Voldemort when others were living in denial, and was never afraid to put his own life on the line. Not to mention Grindelwald. After all, “It takes a great deal of courage to stand up to your enemies, but a great deal more to stand up to your friends”.
Ravenclaw is pretty obvious, too. Dumbledore is one of the wisest and most knowledgeable characters in the series. He’s always full of ideas that are usually very close to the truth and figures things out about five steps ahead of everyone else. Pottermore describes Ravenclaws as “eccentrics” who are “often out of step with ordinary people”, and Dumbledore fits this description as well: from his quirky idea of saying “a few words” (“Nitwit, blubber, oddement, tweak!”) to his willingness to keep on telling the truth even in spite of efforts to silence him, Dumbledore is never overly concerned with how others see him. He is known for breakthrough discoveries such as the nine uses of dragons’ blood, and he always has a better idea of what’s going on than any other character, both due to his vast experience and knowledge as well as his innate intelligence.
Helga Hufflepuff valued fairness and equality, believing – contrary to her three co-founders’ ideas – that all magical children should be welcome at Hogwarts, not simply the bravest or most intelligent or those from all-magical families. This is the kind of attitude that Dumbledore embodies as well, drawing criticism from those who disapprove of his openness. He welcomes muggle-born students to Hogwarts, encourages Hermione in her campaign for House-Elf rights, converses with merpeople in their own language, and made special arrangements to allow a young Remus Lupin to attend Hogwarts even though he was a werewolf.
And finally, Slytherin. As a young man, Dumbledore was tempted by ambition, although he soon changed his mind and opposed Grindelwald instead of fighting alongside him. In his old age, he used some of the same tactics to serve a genuine greater good. He was still extremely clever, and one might even say cunning. He seemed to be able to predict what every character would do before they did it and what to say and do to achieve the outcome he wanted. He definitely had most of the series planned out before it ever happened.
As he tells Harry, “It is our choices, far more than our abilities, that show who we truly are”. Dumbeldore may well have chosen to be a Gryffindor, but that doesn’t cancel out the fact that he could have done well in any of the houses. In fact, one might say that he had the courage of a Gryffindor, the mind of a Ravenclaw, the heart of a Hufflepuff, and the intricate plans of a Slytherin.