"Go on with" is a common phrase used to signify continuing an action or conversation. There are several synonyms that can be used to convey the same meaning. Some of these synonyms include: carry on, proceed, advance, continue, persist, pursue, maintain, and sustain. Depending on the context, these words can be used to replace "go on with" and add variety to your vocabulary. For example, instead of saying "let's go on with this discussion," you could say "let's carry on with this conversation" or "let's pursue this topic further." Incorporating synonyms into your everyday language can make your speech and writing more interesting and engaging.