Decks, Patios, Porches and Docks - Extending basement under deck

Our family room was built with a crawlspace under it (not a full basement). We are interested (if possible) in turning the crawlspace into a full basement, without tearing down the family room. We have a big elevated deck that wraps around our family room and we would love to make the basement even bigger by extending the basement all the way under the deck. That way we can have a much bigger basement (which we plan to turn into a walk out basement). What do people think about decks "sitting" on a foundation? I assume that the foundation under the deck would need to be slightly pitched to ensure water would run off. Any views, tips or ideas?