The phrase "at the edge" suggests being on the cusp of a limit or boundary. Some synonyms to convey this idea may include "borderline," "threshold," "frontier," "brink," "precipice," "verge," "limit," "beyond," "extremity," "rim," or "periphery." These terms convey a sense of being in a precarious position or experiencing the excitement, trepidation, or danger that comes with pushing beyond perceived limits or venturing into unknown territory. Whether it's a physical, emotional, or intellectual edge, these words convey a sense of being on the edge of discovery, change, or something significant happening.