up to your neck vs up to their necks

up to your neck and up to their necks both are adjectives.

Word	Noun	Adjective	Verb	Adverb
up to your neck	No	Yes	No	No
up to their necks	No	Yes	No	No

As adjectives, up to your neck and up to their necks are synonyms defined as:

Other synonyms of up to your neck include neck-deep, up to her neck, up to his neck, up to my neck, up to our necks.

up to your neck (adjective)	up to their necks (adjective)
deeply involved	deeply involved