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Is there any rule in Hogwarts that prevents any expansion of the number of houses there are? And if there isn't, why wasn't a house added for:

  • Dumbledore (with the added advantage that he was a student there),
  • Nicholas Flamel (Inventor of the Philosopher's Stone)
  • Newt Scamander (famed zoologist and author)
  • Amelia Bones (considered to be the best witch of her time).
  • Merlin (arguably the greatest wizard ever)

There may be more deserving candidates about whom I may have forgot, please feel free to add them in.

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    Didn't Scamander get expelled? Probably wouldn't want to name a house after a bad example. – Zeiss Ikon Aug 14 '17 at 17:46
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    So, bad example as a student, but did well in later life. Also, Dumbledore was a loyal Griffindor, he'd probably object to having a house created for him. – Zeiss Ikon Aug 14 '17 at 17:57
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    This question is primarily asking if a rule existed. This isn't primarily opinion based as we can say "Yes, there was a rule", "No, there wasn't a rule" or "We're not told or any rules but here's some evidence we have" – Edlothiad Aug 14 '17 at 18:00
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    amp.reddit.com/r/harrypotter/comments/1k02ti/… my favs are S.P.E.W and Lochkhart houses :D – user68762 Aug 14 '17 at 18:01
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    In real life, most of the time when schools name something after someone, it was already something they were going to create. Hogwarts has never needed a new house, so they don't create one, and therefore they don't name it after anyone. If, however, they need a new building to house phoenixes, they might call it the Albus Dumbledore Phoenix Sanctuary. – DaaaahWhoosh Aug 14 '17 at 18:19
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Probably not - it would certainly be very difficult and not logical.

The four Hogwarts Houses are named after the four Founders of the school, not just any notable wizards. The houses were formed along with Hogwarts itself, one for each founder.

“They shared a wish, a hope, a dream,
They hatched a daring plan
To educate young sorcerers
Thus Hogwarts School began.
Now each of these four founders
Formed their own house, for each
Did value different virtues
In the ones they had to teach.”

- Harry Potter and the Goblet of Fire, Chapter 12 (The Triwizard Tournament)

Many great wizards have come and gone since then, and none have gotten their own Hogwarts House. It's likely that this is an honor that the wizarding world would leave for the Founders and only the Founders. In addition, the Sorting Hat, created by Godric Gryffindor, was only "programmed" to Sort students into the four original Houses.

While still alive they did divide
Their favourites from the throng,
Yet how to pick the worthy ones
When they were dead and gone?
’Twas Gryffindor who found the way,
He whipped me off his head
The founders put some brains in me
So I could choose instead!”

- Harry Potter and the Goblet of Fire, Chapter 12 (The Triwizard Tournament)

Adding more houses would require “teaching” the Sorting Hat the specific traits of the newly invented houses.

Creating new ones could cause debate and result in more Houses than is feasible.

Since the Founders' time, there have been more wizards who arguably would be worth honoring than would be feasible to name Houses after. There are a finite amount of students attending Hogwarts, and with too many Houses, there would end up being ridiculously few students per House. Keeping the Houses limited to the ones created by the Founders limits against this in a reasonable and noncontroversial way. The existing houses already have their own history, so not adding any more would be accepted by the majority of wizarding Britain.

“The four houses are called Gryffindor, Hufflepuff, Ravenclaw and Slytherin. Each house has its own noble history and each has produced outstanding witches and wizards.”
- Harry Potter and the Philosopher's Stone, Chapter 7 (The Sorting Hat)

Even if only the best wizards get a Hogwarts House named after them, this would probably get out of hand quickly. Say Dumbledore and Merlin were to get their own Houses. Then, there could be an argument made that Harry Potter should get his own House, because like Dumbledore, he defeated a very powerful Dark wizard. That's already 7 Houses, almost double the original amount.

Adding a new House would require new additions to the structure of Hogwarts.

Each House has its dormitories (from what we know probably 14 per House - a girls' and boys' for each of the 7 years), its common rooms, and several other House-specific things like the House tables in the Great Hall.

“Welcome to Hogwarts,’ said Professor McGonagall. ‘The start-of-term banquet will begin shortly, but before you take your seats in the Great Hall, you will be sorted into your houses. The Sorting is a very important ceremony because, while you are here, your house will be something like your family within Hogwarts. You will have classes with the rest of your house, sleep in your house dormitory and spend free time in your house common room.”
- Harry Potter and the Philosopher's Stone, Chapter 7 (The Sorting Hat)

Adding a new House would require some restructuring of Hogwarts itself.

The new House may also be near-identical to an original one, depending on who it's for.

As Skooba mentioned in the comments, a new House named for Dumbledore would be very similar to Gryffindor. Taking the example I give earlier, if Dumbledore and Harry both got Houses, there would end up being three different versions of Gryffindor at Hogwarts. This would make the Sorting process much harder, since the Sorting Hat would then have to decide if a student with Gryffindor traits goes into Gryffindor, Dumbledore, or Potter.

If not similar to another House, the new one might be too specific to have many members.

Say we don't name the new House for Dumbledore or Potter, or any other wizards defined by their bravery. Instead, we create House Scamander, the House for students with a passion for working with magical creatures. The problem would be, its only members might be Hagrid and Charlie Weasley, who didn't even go to Hogwarts remotely close to each other. If we were to just make the House traits less specific traits Newt had, though, we'd then have another version of Hufflepuff.

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    One would also likely need to be alive to create their house as to bestow the properties they were seeking into the hat. – Skooba Aug 14 '17 at 18:07
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    Also everyone is already a student there... their qualities would just revert to one of the Founder... e.g. House Dumbledore would just be House Gryffindor Redux. You don't need both. – Skooba Aug 14 '17 at 18:09
  • "Adding a new House would require some restructuring of Hogwarts itself." Hogwarts already reconfigures itself, so that shouldn't be an issue. OK, maybe a few moving staircases isn't what you had in mind, but it's true! – FreeMan Aug 18 '17 at 19:05
  • Right, and there definitely would be a 'Hogwarts House of Malfoy' if they could - plus they'd need loads more teachers to be heads of all the houses. – marcellothearcane Aug 20 '17 at 10:09
  • Oh, and wasn't the sorting hat made with ancient magic that has since been forgotten? – marcellothearcane Aug 20 '17 at 10:10
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It might or might not be technically possible, but it wouldn't be a good idea.

It sounds like you're talking about fully fledged Houses, peers to the existing Four, and this would be troublesome; you'd have to build new common rooms and dormitories, reprogram the Sorting Hat somehow, new Hourglasses, and so on, and there'd be very little to gain from it.

It should also be noted that you've named five possible new Houses, three of which are from a single generation, more or less; Hogwarts has been around for about a thousand years, so at that rate you'd have twenty or thirty Houses by now. I think you'll agree that would be a bit awkward!

To answer the question as asked, there probably isn't a rule in the sense of a magically enforced contract or Wizengamot law, but custom can be a law all of its own, particularly when reinforced by common sense.

[My actual answer ends here.]


Opinion Piece

That said, there is another scenario that would be both more plausible and more beneficial, and that personally I'd have liked to see happen. As Dumbledore said:

You know, I sometimes think we sort too soon!

If they had created four new Houses specifically for first and second year students, assigned at random, the Sorting could take place at the end of the second year. Hopefully, some of the friendships formed in the first couple of years would last, providing bridges between the Four Senior Houses.

You'd still need new common rooms and dormitories, but they needn't be as large, and it would get the youngsters out from under the feet of the older students so there would be practical benefits, not just social ones. You wouldn't (necessarily) need new Hourglasses, I'm not convinced that the Points system works well for younger children anyway, and the Sorting Hat would not need to be reprogrammed, so on the whole this would be a much more plausible change.

The Junior Houses would need names; personally, I'd go with the four teachers killed in the war: Dumbledore, Snape, Lupin, and Burbage.

Not to be, alas. Custom can be a law of its own.

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    I wonder why you think assigning at random would be somehow more beneficial than just sorting by Hat? Incidentally, the wizarding world doesn't seem very good at "random" or math things so I doubt it would be truly random. – Wildcard Aug 14 '17 at 22:36
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    @Wildcard, I don't think holding a lottery is beyond the wizarding world's ability. But it doesn't have to be truly random, heck, you could do it alphabetically if you wanted - just so long as nobody thinks that the people who were put in Dumbledore are inherently better than the people put in Burbage, or vice-versa for that matter. The point of the exercise is to discourage rivalry, not create yet another reason for it! – Harry Johnston Aug 14 '17 at 22:43
  • A distribution method alphabetically based on last name creates family-based House divisions even more strongly than currently. A known distribution method based on first name shifts the onus onto wizarding parents to decide their preference while naming their children. (Interesting effect of a change intended to prevent premature sorting!) Custom usually doesn't need to be overturned. :) – Wildcard Aug 14 '17 at 22:51
  • @Wildcard, realistically, I don't think that would be a problem; for one thing, there's no need to use the same alphabetical method each year or to announce it in advance, even assuming that for some strange reason you can't just use a lottery. But I'm curious as to why you think parents would care enough to try to game the system - you'd only be in a junior House for two years, and it wouldn't affect which of the senior Houses the Sorting Hat puts you in for the other five. I think the focus would remain on the four traditional Houses, and nobody would care much about the junior ones. – Harry Johnston Aug 14 '17 at 23:25
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    What makes you think wizards can't deal with randomness? They've got an entire magic branch to deal with numbers (Arithmancy). That said, the only example I can think of was contestants being matched to random dragons (which also determined the order) for the first task in the Triwizard Tournament, which used the old-fashioned "grab 'em from a bag" strategy. (You'd think wizards would have something more sophisticated than that.) – Llewellyn Aug 20 '17 at 17:40
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As far as I know there is never any mention of any rules about changes to the house system. However, when we look at the reason why the four houses exist, we can see that there would be no point of creating additional houses.

The underlying premise of the question here seems to be that the houses are simply tributes to great wizards and witches. If that was the case then indeed it might make sense to expand the pool of great wizards and witches that are tributed by the houses. However, I think the evidence from the books provides an entirely different reason for the houses.

The reason for the houses (and their names) is not to honor the people they are named after. Rather, the houses were created out of practicality. Hogwarts was co-founded by four individuals: Godric Gryffindor, Helga Hufflepuff, Rowena Ravenclaw, and Salazar Slytherin. These four individuals had different educational philosophies. In order to cater to each of their viewpoints, they divided the school into four separate parts. Essentially there were four separate schools within the school. Each founder chose the students he/she wanted to teach, and presumably taught them what they wanted to teach them. It is possible that a Gryffindor student and a Slytherin student would end up receiving very different educations. Here are the quotes from the Sorting Hat's songs that illustrate this:

From Order of the Phoenix:

These differences caused little strife
When first they came to light,
For each of the four founders had
A House in which they might
Take only those they wanted, so,
For instance, Slytherin
Took only pure-blood wizards
Of great cunning, just like him,
And only those of sharpest mind
Were taught by Ravenclaw
While the bravest and the boldest
Went to daring Gryffindor.
Good Hufflepuff she took the rest,
And taught them all she knew,
Thus the Houses and their founders
Retained friendships firm and true.

From Goblet of Fire:

Now each of these four founders
Formed their own house, for each
Did value different virtues
In the ones they had to teach.
By Gryffindor, the bravest were
Prized far beyond the rest;
For Ravenclaw, the cleverest
Would always be the best;
For Hufflepuff, hard workers were
Most worthy of admission;
And power-hungry Slytherin
Loved those of great ambition.
While still alive they did divide
Their favorites from the throng,
Yet how to pick the worthy ones
When they were dead and gone?
'Twas Gryffindor who found the way,
He whipped me off his head
The founders put some brains in me
So I could choose instead!

When the founders realized that they would eventually die and no longer be able to divide up the school in this fashion, they bewitched the Sorting Hat to take their place. That is to say that the Sorting Hat would divide up potential students in the same way as the founders would have.

Thus, as originally established the houses were not simply a vehicle for fostering team pride, or other such things. The houses had a very specific purpose, which was to assign students to the educational path that would best suit them. Now in the time period in which we see Hogwarts there does not seem to be any real educational differences between the four houses. They all have the same classes, taught by the same teachers, at times even together with other houses. Presumably, at some point in the thousand years between the founders and the time we see Hogwarts, some changes had been introduced. By Harry's time it seems that indeed the houses were nothing more than teams to take pride in, and perhaps a way to keep track of students.

For the original purpose of splitting students by education type there would be no reason to add houses for other famous wizards and witches. The only reason to add houses would be to offer a different style of education, and apparently four houses were enough to cover the different styles. If there were students who didn't quite fit precisely into one category, for all we know they could have joined other houses for certain parts of their magical instruction.

When the system was changed, and Hogwarts became one school with a bunch of teams, the four houses were apparently kept as a holdover from the original system, or as some kind of tradition. Additionally, when the houses are just teams, four is an easy number to work with. With four houses there is sufficient competition, but still a full quarter of the students get to win every year. With four houses each house should have enough students to form a Quidditch team, any other house team or club, provide prefects, etc. If there were ten houses, we might end up with a house that can't field a team, or has no students worthy of being prefects. Four houses also allows the scheduling to be relatively simple; the more houses there are the harder it becomes to schedule classes, sports, practices, etc. without conflict.

There would be no reason to add new houses to honor great wizards or witches, because that was never what the houses were about. Additionally, if more houses were to be added there would certainly be much disagreement about which great wizards and witches should have houses named after themselves. With all the houses being the actual houses established by the founders there was nothing to dispute. Furthermore, once you start adding houses named after recent people, you open the possibility that there might be students who have something personal against the house. For instance if there was a Snape house there might be a Longbottom student who does not want to be associated with the person who bullied Neville for so many years — even if the house is an otherwise good match. So logistically it is just much simpler to keep things the way they are.

Finally, there does seem to me some general reticence in the Wizarding world to change. Aside from some broomstick improvements it seems that they are very much living in the past. Such a society is likely to be one where there would be heavy resistance to such a monumental change as adding new houses to Hogwarts. In the words of Professor Umbridge:

There again, progress for progress’s sake must be discouraged, for our tried and tested traditions often require no tinkering. A balance, then, between old and new, between permanence and change, between tradition and innovation..."

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