>I'm looking for names for cases with the meanings indicated below.
>I do have ideas for some of them, but am not sure. Any help much
>appreciated!
>
>"across"
The term used with Estonian, Finnish etc. is _prolativ_.
>"on top" superessive -- I'm almost certain on this one!
Most of the list seems to agree with you.
>"under"
>"in under"
I fail to grasp the distinction fully here. Is the former supposed to be
directionality-neutral maybe? In that case I'd rather tag subessiv to the
latter instead. But if you mean "to under" & "into under" instead, your
original associations should probably work.
>"outside"
Adessiv should fit.
John Vertical