The phrase "go one better than" is often used to describe a situation where someone strives to outdo another person's accomplishments or achievements. While this phrase is commonly used, there are a number of synonyms that can be utilized to convey the same meaning. Some possible alternatives include "surpass," "outperform," "exceed," "outdo," "outshine," "top," "beat," "eclipse," and "outmatch." Each of these words can be used to indicate that someone has achieved a greater level of success or accomplishment than another person, and they can be especially useful for writers who wish to vary their vocabulary and express their ideas in a more creative manner.