>The enrichment doesn't give us any information about how objects are related, so we can only really get a set, as Anindya points out -- and there's a trivial information-free preorder, the codiscrete preorder, which we can endow on any set. Can you explain where this logic falls through?

Try using set union (\\( \cup )\\) as your monoidal product, and then apply the definition John gave in the first post. The enriched structure that comes out should be an old friend.