"Keeping under one thumb" refers to controlling or dominating a person or situation. There are several synonyms that can be used in place of this phrase, including "exercising control over", "ruling with an iron fist", "holding sway over", "having a firm grip on", "commanding", "domineering", "dictating", "manipulating", and "puppeteering". These words all convey a sense of power and influence, emphasizing the idea that the individual in question is able to maintain a tight grip on the people or circumstances around them. By using these synonyms, you can add variety and nuance to your writing, while still conveying the same basic meaning.