Many languages have some type of differential object marking, even, arguably English, if we consider verb pairs like shoot x vs. shoot at x to be distinguished not by 'shoot at' being a phrase, but by the object phrase containing a preposition. In English, it gets a bit complicated due to being lexically determined to a great extent.
However, other languages have a more predictable system: Turkish, for instance, uses the nominative with indefinite objects, and accusative with definite objects. This is fairly simple. For a more complex system, let's look at ... Finnish. Now, I'm leaving out a truckload of details here.
Finnish uses the partitive whenever the verb is either of
- certain verbs just generally use it
It uses the partitive whenever the verb is all of
This asymmetry between the two is sort of notable:
atelic telic negative partitive partitive positive partitive accusative
Now, let's imagine a language where the differential marking really serves to distinguish a three-valued thing, let's call the values A, B and C. This system only has two surface forms, however. Singulars merge B and C, plurals merge A and B.
However, we could imagine that a language may want to distinguish all three of these on, for instance, pronouns. And we can imagine a multitude of ways that this distinction is done: unique morphemes, reduplicated morphemes, change of roots or some more shenanigansy approach.
1. Unique Morphemes
Trivial, really. whereas regular nouns use two morphemes (whereof maybe one is a null morpheme), the pronouns have a unique case morpheme here.
2. Overlap Elsewhere
A bit like the previous, but here, the pronouns overload some other case here. Maybe the pronouns can use the genitive for direct objects to distinguish this third option, whereas regular nouns can't.
3. Reduplicated Morphemes
A bit like the 'unique' morphemes solution, but simply just have the accusative suffix go twice on the pronoun. A simple alternative would be to have both the accusative and the genitive combine to form this case.
4. Change of Roots
This is an obvious and simple solution, ... but. We can do something interesting about it. Much like the I-me suppletion in English, this would have a unique root involved. However, to make this interesting, we could have one of the object cases conflate several pronouns. For instance, maybe gender distinctions are fewer for the special root? Maybe number is not distinguished in third person? Or even in first person? Or hey, let's be radical and let's not distinguish first and second person at all!