There are many synonyms for the phrase "on the verge." Some of the most common include "at the brink," "on the cusp," "about to," "on the threshold," and "near the edge." Each of these phrases describes a situation where something is about to happen or something is very close to happening. "On the brink" and "on the cusp" imply that something is about to happen that will change things significantly. "On the threshold" means that something is about to happen or that something is about to be reached. "Near the edge" describes a situation where something is close to happening, but it hasn't quite happened yet. Regardless of which synonym you use, they all signify a sense of anticipation or an impending event.