Said by males, mostly, referring to the demand of giving oral sex, preferably at that exact moment in time.

The prefix "dome" is widely know as referring to one's head.
The suffix "box" came from the SNL skit that aired in late 2006 by Justin Timberlake; "Dick in a box".
person 1: Yo foo, ya wanna bounce?
person 2: Hells naw, you see all these bitches up in here?? dome my box you cunt.
by gwazza? March 9, 2007
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