Not sure if I'll finish this because I have a lot of other stuff going on, but I'll give a shot at it.

The game is about polyamory in monogamous social custom, or reconciling a complex sexual self with a simple sexual mores. Every character has several aspects:

Monkey: This is the aspect that just wants to have fun. Spontaneous, physical fun without too much thinking or strings attached.

Puppy: This aspect wants love. Safe, consistent, well-defined, predictable love. Maybe the character was never given enough attention by their parents, or a whole lot which was shut off too soon.

Snake: This aspect wants to assert social dominance. It wants to have the best, it wants to have things because other people have it, it wants others to know it is the best.

Puppet: This aspect wants to have its romantic/sexual identity respected by society and have a strong social status. This is usually done by repressing the aforementioned aspect in favor of some simple and/or idealistic image.

The basic idea is that the players try to fulfill all of their different Aspects, hopefully failing miserably with collateral damage.

Ok, you were losing me until I read "failing miserably with collateral damage" at the end. I'm onboard now :)