The phrase "reign over" implies a sense of domination, control or power. There are a number of synonyms for this phrase that can be used interchangeably, depending on the context. For example, "rule over" can be used to describe the exercise of authority over a group of people or an area. "Dominate" is another synonym that can be used to convey a sense of control or influence. "Govern" is a slightly more formal term that can also be used to describe the exercise of power. "Command" is a term that is often used to describe leadership positions in the military. Overall, there are many synonyms that can be used to describe the idea of "reigning over" something or someone.