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Per Ralph Breaks the Internet, you qualify as a princess if you meet even one of the following qualifications: magic hair, magic hands, animals talk to you, you were poisoned, cursed, kidnapped or enslaved, or if people assume all your problems got solved because a big strong man showed up.
So the question is, who outside of the established Disney Princesses fits this bill?
People often suggest Princess Leia - the clue is in the name, after all. However, I'd like to point out that none of the above requirements mention having to be female, and that Leia's father Darth Vader both has magic hands and was once a slave. Thus he is clearly a Disney Princess.
I'd also like to nominate Thor. Magic hair? Check - watch how he transforms his scraggly hair into a well-maintained and woven thatch in Avengers Endgame. Magic hands? Check - we see him casting lightning bolts from them in Thor Ragnarok. Animals talk to you? Check - he and Rocket have some good conversations. Cursed? Maybe check - Odin stripping him of his powers seems to fit in my opinion. Enslaved? Check - Grandmaster enslaved him. People think a big strong man showing up solves all his problems? Check - at the start of Avengers Infinity War many viewers assumed Thor's problem with Thanos was solved when the Hulk intervened. Thor qualifies on multiple counts, and so is a Disney Princess.
Any other unlikely candidates? Make your cases.
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Aquagirl fits some of the criteria: talks to fish, likely to be saved by Aqualad or at least Aquaman. Finally, and this is what makes her an unlikely candidate: she was poisoned by Chemo; indeed, that's how she died. Or do the rules specify you have to survive the poison?
If survival is not part of the criteria, there are a lot of Disney princesses in the Conan books as well as the works of Shakespeare..
Doctor Doolittle of course counts because conversations with animals is his thing. Actually come to think of it, nearly everyone counts as s Disney princess with the above criteria because humans are a type of animal.
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Since Vanelope only fitted one of the criteria but was accepted as a princess, it's clear that you only need one category to qualify, though obviously the more you hit the better. And since the princesses all survived, you don't need to die from the poisoning, though I don't think failing to survive disqualifies you either.