Welcome to our forum.
I would think the word "quad" would work. It would be relatively unusual if each of the four people was romantically involved with the other three.
Anyway, I'm sure you will find more info as you look around. By the way, I lived in Michigan for about 20 years, so it is nice to see it's a small world.
Glad to have you aboard,
Love means never having to say, "Put down that meat cleaver!"