New CBB

For Finnish, there isn't really enough to establish a pattern.

you have

-ltA -llA -lle
-stA -ssA -(h)Vn
--- -nA -ksi

the -e pseudomorpheme doesn't form any pattern but exclusively pops up in one spot - other than that, the ltA, llA, lle would seem to be a good candidate, esp. as stA ssA starts out just the same; but then you don't get sse at the end of that. and -na and ksi, that in many ways serve similar roles as llA/ssA and lle/hVn - and sometimes in fact can be used for the very exact same meaning - don't help out either.

Thanks.
I mentioned four languages, because my memory doesn't serve to tell me which languages I was trying to remember. I'm pretty sure at least two of those four has the kind of case-system I was thinking of; but I'm not surprised that at least one of them doesn't.

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Turkish has a relatively small case system consisting of but 8 or so cases, and there's no cartesian component like {on, in, under} * {to, at, from} in operation in it. The hungarian system looks like it might have had some more regular underlying function as far as that goes, but it's lost any clear regularity in it too.

Hindi might get close, but it seems the combination of adpositions there isn't entirely straightforward either.

As I know, Hindi is a complicated case of defining cases as Japanese.
It can either have two cases: direct and oblique and several postpositions joined to the oblique case.
Or it can have several cases if the postpositions are defined as affixes.

Historically the Finnish case system consist of two elements the fist being derivational. (There are other thories too)

miehe-lä-nä
man-'place'-LOC
'at husband's house' = 'married'
>miehe-llä
man-ADESS
in man's possession/in man's place