When it comes to referring to influential people in the business industry, there are several synonyms for the term "business bigwig" that can be used. One of the most commonly used terms is "mogul," which is used to refer to a powerful and influential figure in the business world. The term "tycoon" is also often used to refer to someone with significant power and influence in the business world. Other synonyms include "captain of industry," "baron," "magnate," and "power broker." All of these terms refer to someone who has achieved significant success in their chosen industry and who wields a lot of power and influence in their field.