There are multiple synonyms that can be used instead of the phrase 'stay around'. These include 'linger', 'remain', 'stick around', 'hangout', 'persist', 'endure', 'continue', 'survive', and 'remain present'. While 'stay around' is commonly used to express the idea of not leaving a particular place or situation, it can be replaced by any of the above-mentioned synonyms depending on the context. For instance, 'hangout' is often used in a more social context, while 'persist' can be used in a professional setting to imply continuing with an ongoing project or task.