Other terms which express this action include raise a stink and paint the town brown.
person 2: Just go whiz behind the house, nobody'll see you.
person 1: But I gotta free James Brown!
person 2: wanna borrow my mom's Holy Bible to wipe with? The pages are surprisingly soft.
person 1: ok that sounds cool, but how come YOU get to be person 2? I'm the one dropping the deuce!
person 2: Look bro, I'm just a fictional character in a hypothetical conversation which was contrived for the purposes of illustration. Go ask hecktor dangus.