This alcohol must be dangerously delicious and also violently colorful to stimulate the senses accordingly.
“Broadway” is simply to denote the absolute and total debauchery that will undoubtedly permeate the atmosphere (might be mistaken by one's nose as the smell of random sex and fruity vodka). This takes its roots from the connotation that a Broadway show is the epitome of showmanship and live entertainment.
There can be no rules at all for behavior, except those put in place to keep traditional morals out of everyone's minds. Ex) All drink and all clothes must disappear by 2am.
A Broadway Shit Show should be impromptu, but can be planned as long as this planning does not detract from the shenanigans that must occur to earn the gathering this exclusive title.
The only real rule for a Broadway Shit Show, (hence why you probably haven't heard of one before), is that Fight Club rules apply.
::This means that this particular type of shit show must be a total secret to all except the participants, 40% or more forgotten due to imminent head injury (be it physical or chemical), and last but not least completely out of any reasonable human being's comfort zone (hence the likeness to Fight Club's supposed mind cleansing properties).