When we say someone is "up to her neck," we typically mean they are in a difficult or challenging situation. However, there are plenty of synonyms that can be used to convey this same idea. For example, we might say someone is "in over their head," "swamped," or "bogged down." Alternatively, we might use phrases such as "up to their ears," "drowning," or "snowed under" to describe someone who is struggling to keep up with their responsibilities. Ultimately, the choice of synonym will depend on the context and the tone of the conversation, but there are plenty of options available to accurately convey the idea of being "up to one's neck".