It could be said like this, which is not a usual or a common thinking that persists, sometimes a superior one than the common sense. Certainly this has the constraints of not being healthy where a person thinks and he gets in to an action, that might lead him to experience the positive or negative scenarios of what he does.
Common sense, at least according to AI pioneer Marvin Minsky, is not easy to acquire, and one can see the difficulty of AI systems and robots in doing the simplest task.
But assuming that after a certain number of years living in civilized society, one does acquire common sense in order to get along and act "normal" in society, uncommon sense would be the intelligence or judgment exhibited over and above, or outside, of common sense.
Warren Buffett could be said to have uncommon sense, as does Mark Cuban who made it to the billionaire club after cashing out on his Yahoo! stock options right before the Dot Com crash.
However, uncommon business/financial sense is only part of uncommon sense since it might include other "intelligences" such as artistic intelligence, athletic intelligence, even social intelligence (which explains how some people are immensely popular while others cannot easily "seduce" people).
Bill Clinton was such a person, with highly developed social sense.
Uncommon sense, in a business setting, might also be defined with respect to specific business functions like new product development (I've uncommon sense in that I can create new workshops that are highly successful and taught at university), accounting, HR, financing (Bill Nguyen, is a well known entrepreneur who can easily pitch to VCs to get hundreds of millions of dollars), recruiting, etc.
Thanks for a great question!
I would define 'uncommon' sense as being a rarified form of common sense! Some might take this to mean luck or providence, but uncommon sense to me means that you are flexible and can adapt quickly and easily to new circumstances.
I think that can only be built from having good common sense though; in business that means understanding what is on your plate / in your influence right now, what you can change and having clear plans for the future that also have flexibility built in.
I think uncommon sense is earned, not inbred.
Uncommon sense is Logic without emotional influence. People are commonly more emotional than logical (even me and my overly logical self), and blinded by ambition or ego or the smoke and mirrors of societal acceptance. Thus common sense is to senselessness as normal is to insanity. To have uncommon sense is to apply logic unequivocally and to be completely sane is to be abnormal.
I'll be the first - if common sense implies using sound, prudent judgment in a given situation then uncommon sense would be doing the opposite. However, the implication is that in the end it turns out to be a "good" though not an expected outcome. It is like "thinking outside the box" in my opinion!