go somebody one better
go somebody one better {v. phr.}, {informal}
To do something better than (someone else); do more or better than; beat.
Bill's mother gave the boys in Bill's club hot dogs for refreshments, so Tom's mother said that she would go her one better next time by giving them hot dogs and ice cream.
John made a good dive into the water, but Bob went him one better by diving in backwards.
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Source: A Dictionary of American Idioms
