From Longman Dictionary of Contemporary Englishgo one better (than somebody)go one better (than somebody)informalSUCCESSFUL to do something more successfully than someone else The following year Lewis went one better by winning the gold medal. Of course, they had to go one better and have the whole garden redesigned. → better
Examples from the Corpus
go one better (than somebody)• Beth Wolff, president of her own residential real estate company, likes to go one better.• Like an aphid, then, the caterpillar employs ants as bodyguards, but it goes one better.• They have followed each other up the ladder, but whenever he has reached the same rung she has gone one better.• Ford went one better and put 60 two-stroke Fiestas on the roads.• But even if Forbes loses his quest for the Republican presidential nomination, he may still go one better than his father.• She goes one better than last year.• The Bristol & West have now gone one better than the standard endowment mortgage.• Laker's return of 9 for 37 was outstanding, but he was to go one better when the Aussies followed on. 