The phrase "on edge of" can be substituted with various synonyms depending on the context in which it is used. Some possible synonyms include "close to," "near the brink of," "on the threshold of," "at the cusp of," "on the verge of," and "teetering on the brink of." These synonyms can be used to convey a sense of anticipation, excitement, or danger. For instance, one could say "the team was on the verge of victory" or "he was teetering on the brink of financial ruin." Whatever the context, there are many ways to express the idea of being "on edge of" something.