>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

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.

>"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.


Adessiv should fit.

John Vertical