When something "supervenes upon" another thing, it means that it occurs unexpectedly and in addition to something else. There are various synonyms that can be used in place of "supervene upon" such as "take place", "occur", "happen", "arise", "befall", "develop", "surface", and "manifest". All of these words imply an unforeseen event happening that is separate from what was previously happening. These words can be used in a variety of contexts, such as a sudden illness supervening upon a previous injury or an unexpected opportunity supervening upon a difficult situation. Whatever the case, "supervening upon" can be replaced with any of these synonyms to convey the same meaning.