Extremely busy (with something); deeply or overly involved (in something); possessing, filled up with, or overwhelmed by an excessive amount (of something). There's no way I can take a vacation right now, I'm up to my neck in work at the moment! I only meant to be peripherally involved in David's business venture, but before I knew it I was in up to my neck! Dana was worried she wouldn't find any work as an accountant working for herself, but she's up to her neck in clients!