The phrase "goes on with" is commonly used to refer to the continuation of an event, a story, or a conversation. However, there are many other synonyms that can be used in place of "goes on with" that can help to add variety and nuance to your writing. Some examples include "proceeds," "carries on," "moves forward," "continues," "persists," "develops," "advances," "unfolds," "evolves," and "progresses." These synonyms can be used interchangeably with "goes on with" depending on the context and tone of your writing, and they can help to keep your writing fresh, engaging, and easy to read.