EDIT: reposted because of accidental deletion
Consider a situation wherein the case systems (or gender systems, or whatever) differ for singulars and plurals. Now, consider some determiner which semantically is plural-like but formally singular. This happens, sort of, in English, with the determiner 'each'.
Now, let's assume that the case system in the plural makes fewer distinctions than it does in the singular, e.g.
- conflates accusative and nominative?
- conflates locative and dative?
- conflates genitive and comitative?
The exact details are irrelevant - come up with them at your own leisure.
Now comes the twist: the case markers are singular (or at least we omit the plural marker if we're dealing with a more agglutinating language), but follow the distribution and function of plural cases. Thus, 'each' is followed by a formally singular noun with the plural case system. Similar mismatches can of course be enforced with, say, gender systems or any other similar thing.