Deck over Flagstone Patio

We have a 8'x 8' flagstone patio about 3' off the ground from a sliding door in the back of our house. I want to put a composite or treated wood deck over this that is 14' x 15'. I thought if I took the flagstone off, I could level the concrete under the flagstone as best possible and then build on top of it. Any suggestions how I could fasten to the concrete?? I can run joists and posts around the patio, but I don't have enough room between the bottom of the door and concrete base to drill treated 2x4's into the concrete and then put decking into that over the patio. Thoughts??

ALSO, I'm concerned about water run off from the new deck over top of the patio. It is level and the wood would be sitting only 1-2'' off the patio. Thoughts???