There are several synonyms for the phrase "a second time" that you can use to vary your language and express yourself better. Some examples include "again," "once more," "repeatedly," "reiteratively," "doubly," and "twice over." You can also use phrases like "for the second time," "as a repeat," or "in a case of repetition." These synonyms can help you stand out in your writing and communication to convey the message more effectively. They offer alternate ways of expressing yourself, allowing you to elevate your language and communicate more efficiently. So, the next time you're presenting an idea or writing a paper, try switching up your language and use these synonyms for "a second time".