"Run mill" is a vague term that can have several synonyms depending on the context. For example, "run mill" can mean carrying out a repetitive task or job, in which case it could be replaced with words such as "grind," "churn out," "crank out," or even "hammer away." Similarly, "run mill" can also mean to operate or run a business or industrial operation, in which case synonyms could include "manage," "operate," "oversee," or "run." Additionally, "run mill" can also be used to describe an unpleasant or negative experience, which could be replaced with words like "endure," "suffer," or "tolerate." Ultimately, the right synonym for "run mill" will depend on the context and the intended meaning of the phrase.