"Go someone one better" is a phrase that means to surpass or exceed someone's effort or achievement. There are several synonyms for this phrase, such as outdo, outshine, one-up, top, and trump. Outdo emphasizes the idea of doing better than someone else, while outshine suggests doing it with more brilliance. One-up also means doing better, but with a hint of competitiveness. Top means being at the highest level, while trump implies doing better than someone by using one's advantage or skill. All these synonyms highlight the notion of doing better than someone, but each adds a unique flavor to the idea of surpassing someone else's efforts.