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!
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
up to (one's) neck
Deeply involved or occupied fully: I'm up to my neck in paperwork.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.