The phrase "run on" can be used in a variety of contexts and has several synonyms that can be used interchangeably. Some of the most common synonyms for "run on" include "continue," "prolong," "stretch," "extend," and "drag out." These words can be used to describe a conversation, a piece of writing, or even an event that seems to go on for too long. Additionally, "run on" can also be replaced with "ramble," "meander," or "wander" if the meaning pertains to a speech or written work that lacks focus or direction. Regardless of the synonym used, each one encapsulates the idea of something that keeps going unnecessarily.