Pets at Hogwarts appear to be a free for all
Or in other words, wherein J.k. uses them when convenient.
Even though the Hogwarts letter clearly states only three animals are allowed, other animals appear to commonly end up in the castle, including Ron's rat and Lee's spider.
Where those animals go and live is a real big question. Owls have a specific place but what about the cats and toads? Hermione implies Crookshanks will live in her dormitory. But in the 3rd book, Neville straight up has Trever the toad in Potions (which just seems like a terrible idea for a toad known for disappearing. I agree with the general fanfic headcanon that Trever is a magical toad that goes invisible at random). Is it common to take pets to class? Pets appear to have a little bit of a familar style relationship for wizards, as it appears very common for smaller pets like rats and toads to really go nearly everywhere with their owners. So is there always a couple animals in any room? If students regularly go outside the three animalsallotted, what other weird pets are wandering around classrooms?
How about the sheer number of possible animals? If there's around 70 students sharing a dormitory,... well Hagrid said toads are unpopular and he only said cats made him sneeze. So does that mean there's just a dozen or so cats wandering around the dormitory at any given time? I can't believe that only 1 in 70 students would own a cat. Even taking into account owls would be more common sense they were useful for other reasons... let's say around 10 students maybe at least have their own owl, probably mainly the ones that are muggle born and dont have family owls. That's still only 1 in 60 that have a cat. I'm just saying. I'm pretty sure every dormitory looks like a crazy cat lady house with floofers snoozing all over the place.