What's the difference between 可 and 可以?
"可" is a morpheme, while "可以" is a word.

With the meaning of "be able to", "可" and "可以" are interchangeable in most cases.

When we answer a question, we should say "可以", which means "fine", or "OK". When coming to popular culture, some of us would just answer "可", which is not literally supposed to. Say, if you answer like this, we could still understand.

Here are the situations I could come up with, only "可" is used as emphatic adverb (just like "very"), sometimes used to throw a question.
See definition #2 here


For example, "这本书可贵了", which means "this book is very expensive". This is the morpheme "可" used for emphasis.
Another example, "近来可好？", which means "How have you been recently?". This is the morpheme "可" used to throw a question.