When we talk about "most deep-set", we are referring to something that is deeply ingrained or rooted. Therefore, antonyms for this phrase could include "superficial", "shallow", or "uncommitted". If something is superficial or shallow, it lacks depth and may not have a strong impact or meaning. Alternatively, if something is uncommitted, it means that it is not firmly established or deeply rooted. So, when looking for antonyms for "most deep-set", we should consider words that describe something that is not entrenched, firm or fixed, but rather superficial and subject to change.