I will start off by saying I am and 3 people (not names just who they are E.G.: I am your father's cousin's sister's) here's the rules you can only add 3 people at once no more no less so I'll start it off:

I am your father's uncle's sister's

EDIT: I got this idea from an episode of family guy

I am ur mother's grandma's cousin

I'm your cousin's uncle's wife...

...wait, what?!

Moved

I'm your brother's friend's half-cousin!

I am your Dads Dads Dad.
Does that make sense? :D

I am your sister's father's uncle

I'm your second-cousin's half-sister's goat

Seems that game start to be popular, so soon will add it in list of games.

I am your granddad's roommate's in law

I'm your mother-in-law's step-brother's midnight snack...

I am your mother's uncle's nephew