Jacking up house to make crawlspace into lower level?

Short answer: kind of yes.

Take a look at the houses in the Hurrican Sandy flood zone which were raised to keep them above future flooding.

They weren't intending to add a new first floor or basement, but the liftingis the same.

You beat me too it. A lot of homes near the beach here in NJ have been jacked up and are now on pilings high enough for another floor. Like you say, they use that area for parking or a garage, not living space, but the idea is the same. They are even putting the AC units up high now too. But the difference is these are relatively expensive homes at or near the beaches and the cost can be justified. For a house in general, I think it would probably be cost prohibitive. Also, I would think that with jacking, you probably wind up with having to do some repairs to cracked walls and the like that result. You also have to consider that the old and new parts will be used for, ie if you jack and don't change things, the kitchen, LR will be on the second level.

Before undertaking adding a whole story to a house, I'd consider what the market value is now, what it will be after, what the cost of the addition will be. I would think it might make more sense to sell and find another house.

Similar things have been done. In coastal areas a lot of houses have been raised for flood prevention but the new lower level is not a living space, just storage.

I don't know how cost effective it is compared to just moving to a larger house.

When faced with that situation, my parents started digging.

As long as that doesn't produce an indoor swimming pool - - -

It did most springs or sometimes during the January thaw. When I was a few months old my parents went to stay with my uncle when the water got above the coal grate. You just learned to keep an eye on the creek and start moving your toys to high ground.