The phrase "make a big thing of" means to emphasize or exaggerate the importance of something. However, if you want to add a little variety to your language, there are several synonyms you can use instead. For example, you could say "magnify," "blow out of proportion," or "overemphasize." Other options include "make a fuss over," "amplify," or "inflate." Ultimately, the best synonym for "make a big thing of" will depend on the context in which you are using it and the tone you want to convey. Whether you opt for a straightforward term or something more colorful, the key is to use language that is clear and effective in getting your message across.