It all comes down to money. It shouldn't be a problem for a house moving company to raise your existing garage enough to put in two more courses of block. Once that was done, if your current floor has no voids beneath is, I see no reason why you couldn't pour a new floor over the old. In fact, if you wanted to change elevation, a sand fill on top of the existing floor could do that. Again, it all comes down to money.

If you did use a sand fill, then floor heat would be an option.