There are a multitude of synonyms for the phrase "hanging upon," each with slightly different connotations or implications. Other phrases or words that could be used to replace "hanging upon" include "depending on," "relying on," "counting on," "hinging on," "resting on," "riding on," "contingent on," "predicated on," or "conditional on." All of these synonyms suggest a sense of the outcome being uncertain or dependent on something else, whether that be another person's actions, a certain event or circumstance, or some variable outside of one's control. The choice of synonym depends on the nuance or emphasis one wishes to convey in their writing or speech.