absolutive, which marks the object of a transitive verb and the core object of an intransitive verb;
ergative, which marks the agent of a transitive verb;
abessive, which marks a lack of the marked noun;
partitive, which marks a noun selected from a larger group;
vocative, which marks an identifier;
dative, which marks the indirect object of a transitive verb or the recipient or beneficiary of an item or action;
genitive, which indicates a noun as modifying another noun;
instrumental, which marks the means by which the subject does something;
equative, which marks comparison;
egressive, which marks the beginning of an action;
terminative, which marks the end of an action;
temporal, which marks a time;
ablative, which marks motion away from something;
allative, which marks motion onto something;
comitative, which marks companionship or grouping;
elative, which marks motion out of something;
illative, which marks motion into something;
inessive, which marks motion inside something;
lative, which marks motion to something; and
perlative, which marks motion through, across, or along something.
I've been taking a closer look at your local cases (those) that usually express spatial movement and/or location). Customarily, local cases can be divided into:
(1) Those that express movement to something.
(2) Those that express movement from something.
(3) Those that express location.
One could also add: (4) those that express path, or movement across something, but I'll focus on (1)-(3).
When it comes to (1), you seem to have a three-way distinction, between illative (which we may call an 'inner local case'), allative (which we may call an 'outer local case'), and lative (which we may call a 'general local case')
What's your rationale for distinguishing these three? Do you need a general lative case, if you have an illative and an allative case? In what situations would you used the respective cases?
When it comes to (2), you only seem to have a two-way distinction, between the 'inner' elative and ablative. I assume that The ablative may correspond to both the allative and the lative. Am I right? But then why do you only have a two-way distinction among the 'from'-cases, when you have a three-way distinction among the 'to-cases'?
When it comes (3), you list a general 'locative' case. You also list an inessive case. This could be interpreted as an 'inner' case, corresponding to the illative and the elative ones. But you say it's for motion rather than location, which is a bit confusing. You later add an 'adessive' case, which would presumably be the 'outer local case'.
Motion from: Motion to: Location:
'Outer' ablative allative (adessive??)
'Inner' elative illative (inessive??)
'General' (ablative??) lative locative
Does the above table accurately represent your system of local cases?
auxiliary, for the arguments of auxiliary verbs
Which argument? The subject? The object? (But wouldn't the object of an auxiliary verb typically be a verb phrase??). Can you give any example sentences to show how this case works? (The same also for your other cases; it'd be much more interesting with sample sentences than just a long list of case names.)