"Having a hold upon" can be expressed in different ways to provide variation and avoid redundancy in writing. One possible synonym is "gripping," which suggests a firm grasp or control over something or someone. "Dominating" is another option, indicating a stronger or more forceful hold upon something. "Influencing" is also a suitable choice, in the sense that one has the power to affect or change the course of events. Other possible synonyms include "controlling," "manipulating," "commanding," and "steering." Each term has its own nuances and connotations that can help convey a more precise or nuanced meaning in a given context.