The phrase "take on over" is a commonly used expression that means to assume control or responsibility of something or someone. There are various synonyms that can be used in place of this phrase, including "take charge of", "take control of", "take over", "assume responsibility for", "be in charge of", "manage", "lead", "supervise" and "direct". Each of these words can be used in different situations and contexts to convey a similar meaning. By incorporating these synonyms into your vocabulary, you can add variety and depth to your writing and communication, while conveying your intended message more effectively.