The phrase "improve on" means to enhance or advance something that already exists. There are various synonyms for this phrase that can be used to convey the same meaning. One such synonym is "amplify," which implies the act of making something greater, stronger or more extensive. Another alternative is "refine," which suggests the process of making something more precise, polished or pure. "Augment" is another substitute that implies the act of increasing something in size, volume or intensity. "Upgrade" is another synonym that suggests improving an object or system by incorporating latest technology or making certain modifications. All of these synonyms are useful when looking to communicate the idea of improving something.