The phrase "on the brink" typically refers to being on the edge of a significant change or event, usually negative. There are several synonyms for this phrase that can be used to convey similar meanings. For instance, the term "on the cusp" can be used to describe a situation where someone is on the verge of making a significant decision. "Teetering on the edge" and "standing on the precipice" are also great synonyms for this phrase. Other options include "hanging by a thread," "on the verge of collapse," and "at a critical juncture." Whatever phrase you choose, each synonym conveys a sense of urgency and importance.