The phrase "have a hold upon" is typically used to describe having control or influence over a situation, person, or thing. This phrase can be replaced by a variety of synonyms that convey similar meanings. For example, one could say "have a grip on," "have a hold on," or "have a grasp of" to suggest a level of control or understanding. Other synonyms might include "dominate," "command," or "direct." These words all capture the idea of having power or authority over something. Additionally, one might consider words like "influence," "sway," or "impact," which suggest a subtler form of control or hold upon a situation or individual.