>Was he just a one-trick pony?
If knowledge of multiple European languages (not only in their present-day form, but in their historical forms too) is just one trick, it's a pretty big one.
It's an interesting question though. He did own a Assyrian-Babylonian grammar and workbook. It's in this (very partial) inventory of his library.
I'm sure he must have had some knowledge of Sanskrit, given its importance for Indo-European philology though - there is, in fact, a book on Tolkien and Sanskrit which argues that his knowledge of that language influenced nomenclature in the Silmarillion.
However, his academic work was primarily on the Germanic languages, his knowledge of other Indo-European languages varied, and he had some knowledge of Uralic languages, like Finnish.