The phrase "on the ragged edge" typically connotes a state of instability or being on the brink of a breakdown. Synonyms for this could include "on the brink," "on the edge," "teetering on the brink," "walking a tightrope," "on the verge," "at the precipice," "in a precarious position," "on the cusp," "on the brink of collapse," or "on the brink of emotional exhaustion." Each of these phrases captures the idea of being in a precarious or risky situation, potentially with significant consequences. Despite the negative connotations, these phrases can also be used to describe a situation where someone is pushing the limits and achieving great things.