Jocular name for a suit, particularly one worn by businessmen. The three pieces are the jacket, tie and waistcoat, as in a three piece suit, but the cage refers to the fact that one has sold themselves to a life of slaving away for a corporation whereas those who don't wear one to work are free.
"I like my six-figure salary at the hedge fund, I just wish I didn't have to wear this three-piece cage."
The leading piece of a turd which protrudes from the anus often causing the skid mark. Can also be used to describe a person who may otherwise be referred to as a douchebag.
"I asked that chick what she thought of Brian and she said he was a total leader piece."