Something that looks sort of vaguely like this if you squint really hard is attested in real languages, but let's make a more distilled form of it. Consider the most core case distinction in many languages - nominative vs. everything else. Some nouns are more likely to be subjects whenever both a subject and some other NP is present, some are more likely to be objects. We basically get a subjecthood hierarchy, which quite probably is not very unlike an animacy hierarchy.
I imagine that this language has but two cases, and the case of the direct object is also used with adpositions and for any oblique uses. Possession could go any which way, maybe with the subject case being the genitive case as well.
For nouns high up in the hierarchy, the nominative is unmarked, and the accusative is marked. Lower down in the hierarchy, the situation is reversed.
Let us use the same case marker for both and call this the 'INV' case.
I see you.INV
man sees stone
knight fought windmill
windmill.INV killed knight.INV
In intransitive clauses, this offers several options. First a nominative-like approach and an ergative-like approach exist. The nominative approach would have subjects marked the same as in transitive clauses, thus
windmill.INV burns
man falls
The ergative approach would instead produce this outcome:
windmill burns
man.INV falls
We now need to provide an analysis of what's going on under the hood of this system. The nouns will be given two 'classes' – ones high up in the hierarchy are 'I', and lower ones 'II'.
I II nominative direct inverse accusative inverse direct
The ergative situation is similarly
I II ergative direct inverse absolutive inverse direct
The final situation we can consider is an underlyingly tripartite system
I II transitive subject direct inverse intransitive subject ? ? transitive object inverse direct
This provides us with many options! We can now introduce a split-S type of thing, and we can even do that in multiple ways. We can let 'inverse' signal lack of volition (or whatever, but that's a good go-to example), or we can let the opposite of the transitive subject marking signal lack of volition. Thus, we may have a situation where:
I.INV fall
signals lack of volition, but
fish jump
signals volition, OR
I.INV fall
signals lack of volition BUT
fish.INV jump
signals volition
Fluid-S is afaict typologically less common than a lexically-conditioned split-S, but fluid-S is easier to make a toy system out of in just a couple of words. For a lexically-conditioned system, way more options exist, of course: some verbs maybe require direct from all nouns, some require inverse, and some require object marking (thus direct from type II nouns and inverse from type I nouns). Basically, the types of language you can imagine form the following set:
Take as possible verb types the set V, consisting of :
D = verbs requiring direct subjects
I = verbs requiring inverse subjects
O = verbs requiring object-forms out of their subjects
S = verbs requiring subject-forms out of their subjects
The languages we can imagine then forms the set P(V), i.e. the power set of {D,I,O,S}. This is {{}, {D}, {I}, {O}, {S}, {DI}, {DO}, {DS}, {IO}, {IS}, {OS}, {DIO}, {DIS}, {DOS}, {IOS}, {DIOS}}.
A language described by the set {IOS} would then be one that has verbs requiring inverse case subjects, verbs requiring object forms and verbs requiring subject forms.
We can also have a situation where all subjects of intransitive verbs just are direct - i.e. no marking whatsoever.
I II transitive subject direct inverse intransitive subject direct direct transitive object inverse direct
A situation where both I and II are inverse for the intransitive subject is conceivable, but unlikely and not significantly different from this situation - it would merely be a 'cosmetic' difference.
We can also have a situation where the cut-off between I and II is different for the intransitive subject than for the other two (heck, one could experiment with having that cut-off in different spots for subjects and objects too!)
And of course, we can always add in complications with regards to topics - maybe all topics are unmarked regardless of syntactical role?
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