Math nerd here. It's not n!. (Try it with 4 people.) It's n*(n-1) not including self relationships.

While adding people to fix a problem is generally a terrible idea, sometimes adding another relationship creates a stabilizing force that decreases overall drama for all involved. Here's a simple example without romantic relationships involved. I used to live in a large household of friends. We had only one extrovert in the group though. That extrovert was a really useful addition, because he was willing to accept always being the one to pick up the phone or answer the door or call places to place orders for delivery - tasks most of the rest of us hated. But having a house extrovert allowed the rest of us to avoid strangers during our at-home relaxing time, while still having various options and things dealt with. Similarly, sometimes another relationship fills a gap really well, being willing to do things with the other people that they are each separately interested in, but don't have overlap with each other - thus making both people happier.

Sure, every relationship you have is a potential source of drama and problems. But it's also a potential source of emotional comfort and stability, a potential source of entertainment and cheer, a potential source of skills and advice. There;s a reason that people sometimes collaborate - other people can be useful and pleasant sometimes.

@12 Funny, I know of poly relationships past the five year mark.