To break on is a phrasal verb that can mean to enter suddenly or unexpectedly. There are several synonyms that can be used instead of break on, depending on the context. One possibility is burst in, which is often used to describe a sudden intrusion into a room or situation. Another option is appear suddenly, which can be used to describe someone who seems to materialize out of nowhere. Other synonyms for break on might include storm in, barge in, or intrude. In general, all of these words convey a sense of suddenness and unexpectedness, and can be used to create dynamic images in writing or speech.