The Badger And The Snake

What if the four founders had descendants starting Hogwarts the same year as Harry Potter? Four children had been left on the doorstep of different orphanages at a few weeks old, a none one ever found out their origins. Surely, though, the surname matches the house? In a world where the houses are more divided than long division, can the four children teach the school that, really, your house doesn't define you, you define your house?