Looking for old fic with interhouse unity

Very old fic - at least a decade old!

All I remember is that Harry and his friends created a secret club for all Hogwarts Houses where they played a game together and formed friendships - and I think Flitwick was super supportive?

I can’t remember any details about the game, but it wasn’t Quidditch or gobstones or chess. It was something the author made up.