"Burst in upon" is an expression used to describe an unexpected or abrupt entry into a situation or place. There are several synonyms that can be used to convey a similar meaning, such as "barge in," "storm in," "crash in," "burst into," "enter abruptly," "rush in," and "intrude." These words can be used interchangeably to add variety to your writing and convey a sense of urgency or drama. It is important to use synonyms skillfully, however, and not overuse them to the point of repetition or confusion. Ultimately, choosing the right synonym for "burst in upon" will depend on the context and tone of your writing.