There are many synonyms for the phrase "big man" that can be used to describe someone who is influential, powerful or significant. Some common ones include "heavyweight," "bigwig," "tycoon," "mogul," "baron," "leader," "boss," "chief," "captain" or "kingpin." These words convey different nuances of meaning, depending on the context in which they are used. A "heavyweight" implies strength and dominance, while a "mogul" suggests wealth and business acumen. A "leader" implies guidance or direction, while a "kingpin" implies control and authority. Overall, synonyms for "big man" can help to add depth and flavor to your language, providing a more varied and nuanced way to convey ideas and concepts.