There are several synonyms for the phrase "make an inquiry" that can be used in a variety of situations. One of the most common synonyms is "ask a question," which is self-explanatory and straightforward. Another useful synonym is "seek information," which emphasizes the search for answers or knowledge. "Request clarification" is another good option for an inquiry that needs further explanation. "Delve into" is a slightly more formal option that suggests a deeper investigation or research into a topic. Finally, "investigate" is a powerful synonym that implies a more rigorous and thorough examination of a subject. By using these synonyms, you can add variety and nuance to your communication and improve your ability to gather information effectively.