In a Twin Peaks episode you can hear the following question: “So, Mr. Wheeler, what is it exactly you do do?”. It seems to me quite weird. Is it correct?
I suppose that the purpose of the second do isn’t to emphasize something.
Asking ‘what is it exactly you do do?
Is a way of differentiating from ‘what you don’t do’. (Or indeed, whether you do anything at all!)
‘I am a plumber, but I don’t fix pipes, water heaters or baths!’
Reply ‘what is it exactly you do do?’
‘Well I only do radiators actually. And only on Wednesdays. If I’m not busy!’