The opposite of over-prize can be expressed in a variety of ways depending on the context. If we are talking about valuing something too highly, then the antonyms could be 'undervalue', 'underestimate', or 'disparage'. Other options might include 'neglect', 'overlook', or 'ignore'. In some cases, we might use words like 'relegate', 'deemphasize', or even 'abandon'. Essentially, the antonyms for over-prize are those words that convey a sense of underestimating or undervaluing something, whether intentionally or not. By understanding these antonyms, we can better appreciate the nuances of language and how words can be used to convey different meanings depending on the context.