That would be a mistake, IMO. "Case marking" has a specific meaning, and presupposes that a language has case (e.g. "nominative", "accusative" or whatever). There is some relationship between case and thematic rule / grammatical function, but they are not the same thing.
Alright, Greg hit the button before me. But, case is a morphological modification of a word -- not necessarily a suffix, so it could be a prefix, infix, or "mutation".
The primary concept that is relevant here is, roughly speaking, about how some nominal element relates syntactically to other elements of the sentence -- I'm being deliberately open-ended. One example is the relationship between "Bill" and either "cat" or "sold a cat" in "Bill sold a cat". That relationship can be indicated by word order (as in English), by some kind of abstract featural property realized as morphological affixation of some kind (as in Russian or Kipsigis), or by a seriously complicated system of gender agreement patterns in Khoekhoe; and there are other ways. In English, certain syntactic relations are primarily signalled by word order (and there is very little, though not no form-changing as is the case in Chinese). In Sanskrit and Walpiri, these relations are signalled via affixation (and not so much with word order).
The general form of the question that you're raising seems to be, what are the possible value-pairs of X and Y in the linguistic statement "X can be used to signal Y"? My conclusion is that "X,Y" can in principle be anything. There are no doubt database lacunae in finding all logically possible examples.
Now, the term "case" is conventionally used to cover a particular X,Y relationship. The "means of signalling" is diverse, but can be covered by "concatenation of elements", cashed out as an affix or near-affix (like a clitic), or an abstract feature that may spread through a phrase: it would not include governance of verb agreement or word order. The "thing signalled" is about a relationship between a nominal and other things -- back to the open-ended thing. First, that relationship can be just semantic, not structural. A simple example is that one-word answers to questions about subjects take nominative, about objects take accusative, about locations take locative, and so on, in Saami and Russian (as I understand), and maybe in most languages (not all). Second, in a number of Iranian languages, the relationship between elements in an NP, i.e. nouns and adjectives, is marked with an "Izafe/Ezafe" suffix -- so it's not just about NPs and other NPs or VPs. And sometimes a case can't really be said to mark a relationship between a nominal phrase and something else -- so in Saami, the essive case expresses notions like "Being an N", "As as N".
The doomed, gloomy picture that I'm painting arises from the fact that the concept "case" stemmed from observation of properties of particular set of languages with morphological affixation, and the coherence of "case" in those languages (German, Sanskrit, Finnish, Arabic etc.) is morphological (i.e. (Classical) Arabic nouns can't be simultaneously marked nominative and accusative). Problem arise when you partial analogies between some new system and a more classical case system.
As you can probably tell, I don't think that "case" is a generally-useful concept for clarifying that relationship, instead I think one is better off looking at the thing signified, or the means of signifying, depending on whether your interest is more in semantax or morphology.