The phrase "under any circumstances" is often used to indicate that something is not negotiable or cannot be changed regardless of the situation. There are many synonyms for this phrase, including "in no way," "nevertheless," "regardless," "no matter what," "come what may," "notwithstanding," "in spite of everything," and "without exception." These phrases all convey the idea that something is absolute and should not be questioned or altered. Whether you are writing an academic paper, a legal document, or a personal statement, using these synonyms can add depth and nuance to your language and help you to express your ideas more clearly and effectively.