"Up to the ears" is an idiomatic expression used to describe being very busy or overwhelmed with tasks or responsibilities. There are several synonyms to this phrase. One of them is "swamped," which means being overloaded with work or having too much to do. Another synonym is "snowed under," which refers to being buried or overwhelmed by a high number of tasks or responsibilities. "Bogged down" is also a synonym, which means being stuck or trapped in a difficult situation. Lastly, "inundated" is another synonym, which means being flooded or overwhelmed with a large amount of work or requests. All of these words are perfect synonyms that can be used interchangeably to describe being up to the ears.