Why isn’t the soul (ψυχή) considered to be a “person” (ὑπόστασις)?

From my understanding, the unity of spirit, soul, and body is considered to be a ὑπόστασις, or “person.” But, what argument is there against the soul itself (apart from the body) being a ὑπόστασις? It seems the soul possesses reason. It exists by itself. So, why is it not considered to be a ὑπόστασις? Or, if it is considered to be a ὑπόστασις, where and by whom is such an argument affirmed? I am particularly interested in an answer in accordance with Catholic beliefs. **NOTE**: To clarify, I am using «ὑπόστασις» as an equivalent to the Greek πρόσωπον and Latin *persona* as understood in Trinitarian creeds and theology.