The phrase "annoy greatly" can be interchanged with a variety of other words to express a similar feeling of frustration or irritation. Some possible synonyms include "exasperate," "irritate," "aggravate," "vex," or "bother." Each word brings a slightly different connotation, with "exasperate" conveying a more intense feeling of exasperation, "irritate" suggesting a more surface-level irritation, and "aggravate" indicating a frustrating escalation of a situation. "Vex" implies a more puzzling or mystifying annoyance, while "bother" can be used to express mild irritation or dissatisfaction. Overall, the wide range of synonyms available for "annoy greatly" allows for nuanced expression of one's feelings.