up to their necks vs up to his neck

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

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

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

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

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