drip edge underlayment
anything is possible, it just takes money. This one would be no exception.
If there is no void to insulate the interior then you overframe the existing wood deck, install rigid polyiso or eps (styrofoam), THEN sheet over the top of that, then install the roofing. Don't normally do it on average houses as it is quite a costly process but do it quite often on new construction of upper end homes. The insulation alone will run around $2/sf, then add all the framing, sheeting and labor costs, including redoing all the facia to account for the 7-9" heighth of the system.