The phrase "stay up" refers to staying awake for an extended period of time, often past one's usual bedtime. Some synonyms for this phrase include "remain awake," "not sleep," "keep alert," and "be wakeful." Other alternatives for "stay up" include "pull an all-nighter," "burn the midnight oil," or "keep vigil." These expressions suggest the need to work hard or accomplish something that requires one to stay up late. Alternatively, "stay up" can also refer to staying in a particular place or position, for which synonyms include "remain," "linger," "prolong," or "continue." Overall, there are many different ways to express the concept of staying up, depending on the context and specific meaning intended.