up to her neck vs up to their necks

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

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

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

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

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