up to neck

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*up to one's neck (in something)

 and *up to one's ears (in something); *up to one's eyeballs (in something)
having a lot of something; Fig. very much involved in something; immersed in something. (*Typically: be ~; get ~.) I can't come to the meeting. I'm up to my neck in these reports. Mary is up to her ears in her work. I am up to my eyeballs in things to do! I can't do any more!
See also: neck, up

up to (one's) neck

Deeply involved or occupied fully: I'm up to my neck in paperwork.
See also: neck, up