It would really require that Harry acquire friends from different houses. It's not as if leaving any of the virtues unrepresented would be wise in a team setting.
The aim, of course, would be that all the main characters acquire all four virtues (sufficiently) because there's no way to be a hero without all four. If you can't tell right from wrong, if you can't control your passions, if you can't control your appetites, or if you do not intended to do all people their due, you can't be a hero because you will endlessly do wrong through any one of those flaws.
But just like Dorothy in The Wizard of Oz has two characters who represent the heart and the head, Harry would need friends to represent all four.