The phrase "brings up on" is most commonly used when referring to a topic or subject that someone starts talking about or mentions. Some synonyms for this phrase include "introduces," "raises," "broaches," "initiates," "instigates," and "propels." All of these synonyms indicate that someone is initiating or starting a conversation or discussion about a particular topic. Other related synonyms include "mentions," "cites," "references," and "calls attention to." It's always helpful to have a variety of ways to express oneself in conversation, and these synonyms for "brings up on" can help to keep discussions interesting and varied.