Is it possible to build a one-side sloped roof over your existing one? then build a return around the edge so it looks flat. Guttering is encased in the return (sorry if the terminology is not correct, right now I cannot remember it in either language)

I live in Europe so perhaps codes are different - worth checking first.

Not sure I understand. Could you send a sketch or pic of what is being suggested. It would be possible to build over existing however.

Sorry not on the right computer to do this, will do so tomorrow....