1(Harry Potter)

What if the information about the founders was wrong but the traits favoured by the houses were somewhat correct?

Salazar was the sweetheart and in his house ended mostly abused children which he helped and made sure they would grow into cunny and powerful people so they would never again feel weak as they did in front of their abuser(s).

Godric was the one who owned the basilisk(which he let Salazar help take care of) and judged others very harshly as he had been a soldier and knew not to trust people(even children) easily so he picked those who thought themselves courageous and the best of the world to show them humility and that not everything was as they believed.

Helga was pretty smart and enjoyed creating knew spells/potions/etc and she took the ones pushed to the side or hard working to give them a purpose and show that they could go far as long as they kept a balance in their life.

Rowena was a battle maniac who loved to fight but also to discover new things so she took in those who were smart and book focused to show them that there were many more things outside those books and that you may be smarter but there are people who will know more than you about different things.

And what if during Harry's time at Hogwarts, for some unknown reason the founders ended up there or they were disappointed on how things were going on the school they founded and took possession of four teachers/students' bodies(with permission) to judge Dumbledore and others over their actions and help all the children present.

Ships and things like that would be up to the writer but I would be thankful if somehow Harry wasn't made all the founders heir or it centred mostly on him as that is something I see too often and it gets a bit tiring. Use rarely used characters as the heirs and person possessed(ex: Ron, Susan, Hannah, Cho, Marietta, Goyle, Blaise, Lee, etc) and make it centre in other students possible trauma and lives too.