I don't think "сугубо" can mean anything else than "исключительно", "крайне", "абсолютно" (exceptionally, absolutely).
I can't think of any other usage than "Это сугубо конфиденциальная информация".
I wouldn't recommend that you use it interchangeably with "особенно".

Nonetheless, "сугубо" is a $64 word to me. I prefer a simplier word "очень".