Does "It ought to be the case that X" imply "It ought to be the case that it ought to be the case that X?

For example: Fraser Allonby ought to put a sock in it. But ought it to be the case that Fraser Allonby ought to put a sock in it? He certainly ought to be a gentleman. But if he was a gentleman, it wouldn't be the case that he ought to put a sock in it.

Oh dear Christ I oughtn't to have written "ought" so many times. I can't tell whether any of what I've said is correct English.

Very oughtful.

In my view, it ought not to be the case that I ought not to fail to refrain from putting any sock anywhere other than in "it". Do you agree?