Play on words with the Channel 4 (UK) show "Come dine with me" A show in which contestants host dinner parties and rate each other on things such as food quality, hospitality, entertainment etc.
Come down with me is more of the same but is based on an entirely different platform.
DEFINITION: After a night out with friends you return to one of your friends homes after you have been drinking/smoking/snorting copious amounts, and intend only to 'crash' or 'mong out' as you will more that likely feel like total shit and want to be left alone to sleep, eat or throw up.
In the following hours or the following morning you will rate the persons hospitality out of 10 on how you stay was, taking into account things such as: Bed comfort, food, toilets, other guests and of course, your all round experience
"I can only rate Mark's a 7 on Come down
with me because those slut
s wouldn't leave me the fuck alone while i was trying to mong out
and sit and eat Doritos"
"Come down with me tonight dude, i'm so fucked"