Recent literature has claimed that while coordination may give rise to agreement asymmetries, case is always symmetric among the conjuncts in a coordinate structure (Weisser 2020). In other words, a predicate may agree with only one conjunct, but all conjuncts are predicted to realize the same case features. This paper offers evidence against this claim, showing that both types of asymmetries can be found. I then reflect on the wider implications of this data for the relation between case and agreement. The purported lack of case asymmetries but existence of agreement asymmetries has been taken as evidence that case should be evaluated based on syntactic hierarchy, while agreement can be at least partly postsyntactic. Given this reasoning, it follows that analyses that regard case as a byproduct of agreement are incompatible without additional stipulations. Although this paper establishes the existence of both case and agreement asymmetries, I show that the data pose similar issues for traditional analyses of case as a byproduct of agreement, but align readily with those that regard case as a precondition for agreement.