go one better
US /ɡoʊ wʌn ˈbɛtər/
UK /ɡoʊ wʌn ˈbɛtər/

1.
to do something better than someone else, or to improve on something that has already been done
:
•
After his rival scored a goal, he managed to go one better and score two.
•
The new model of the car aims to go one better than its predecessor with improved features.