I've had two professors at different universities who used the terms "super" and "hyper" used instead of "doubly" or "double" to refer to intervals which are a semitone (half step) larger than augmented—or smaller than diminished.
I am not asserting that this is "correct" or "standard" or even a "known & accepted variation"; however, it is something which you (or anyone) may encounter at some point. One was not a native English speaker and both were trained in non-English speaking schools/countries; I assume that is a factor.
I think most people would be able to figure this out, but someone inevitably asked what the heck they were talking about every time I heard them use the term—although, in those contexts I suspect the same question would have been asked if they used the standard terminology.
I argued the point to one of them that "hyper diminished" is actually incorrect and makes not sense at all. I asserted that if he insisted on using substandard jargon, he should at least use it correctly and say "hypo diminished". This started a drawn out discussion among most of the class which was eventually "settled" by an English professor (confirming my position).
This reminds me of a little game I used to play with a high school buddy of mine: "What would be the key signature of…?" (followed by some ridiculous key like: B double-sharp minor) We used to say that we should have unique, dedicated words for "double-flat" and "double-sharp", as well as "doubly diminished" and "doubly augmented".
Apparently, there are several languages which had those words but they have fallen out of use—I believe German or Russian was one of those languages.