"Run by" is a common phrase used to describe the person or entity in charge of an operation. However, there are many other synonyms for the word "run by" that can add variety and specificity to your language. For example, "managed by" or "administered by" convey a sense of control and oversight. "Supervised by" implies a more hands-on approach to management, while "directed by" suggests guidance from a central figure. Other potential synonyms include "headed by," "led by," "steered by," "governed by," "chaired by," and many more. By expanding your vocabulary, you can add nuance and clarity to your writing and conversation.