"Up to his neck" is a common expression used to describe someone who is deeply involved or heavily burdened with a task or situation. There are a variety of synonyms that can be used to convey the same meaning, depending on the context and level of intensity desired. Some examples include "swamped", "overwhelmed", "buried", "immersed", "drowning", "submerged" and "snowed under". Each of these words highlights the sense that someone is deeply, completely mired in something and may be struggling to keep their head above water. Whether used in casual conversation or formal writing, synonyms for "up to his neck" can help convey a sense of urgency and importance.