I had an idea a while ago for a case system that includes one case that just means "not an argument of the verb", while nouns in any other case are assumed to be direct participants in a verbs argument structure. It would be used for adverbial adjuncts, genitives, and objects of adpositions. In such a system one might have, for example, a locative case which could only be used with verbs that select for a locative argument of some sort. Expressing location as an attribute of some other noun would require some other construction (possibly an adposition with "not-an-argument" case). I got thinking about this again last night and decided that it seemed a little odd (not at all unnatural, just odd) because there's this one case that doesn't behave quite like all the others; perhaps it shouldn't really be a case at all. Perhaps it makes more sense for "not-an-argument" to be expressed by a difference in state, orthogonal to case. That would allow "not-an-argument" things to be marked with other cases, separately from their status as arguments, which I think turns out to actually have some neat disambiguatory uses. Most obviously, it allows you to distinguish adverbial and adjectival adpositional phrases: "I saw the man with a telescope." -> "I used a telescope and saw the man." "I saw the man with a telescope-NAA." -> "I saw the man who had a telescope." -l.