up to his neck vs up to our necks

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

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

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

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

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