When trying to express the idea of "building on," there are various synonyms that can be used to convey a similar meaning. For instance, you can say "expanding upon," which means the same thing as growing something that already exists. Alternatively, using "developing" suggests improving upon an existing element, while "advancing" implies a progression to bigger and better things. Moreover, "taking further" can be used to express the idea of building on something by taking it to the next level. Finally, "continuing with" similarly conveys the sense that something has been started, and you are adding to it by carrying on with what is already in place.