I have raised a coulple of wood houses here and leveled a few. Wood is much lighter than concrete and there was a crawl space to begin with. Looking back, I wonder how we kept from getting someone killed even at that.
Your concrete weighs 2 or 3 times as much and no crawl space from which to access it. You will need several 25 to 50 ton jacks and I wold want a steel beam to lift with, but then, there is the danger of the slab breaking when it is raised. Yes, you could add to the piers as needed; just be sure they are resting on "hardpan" undisturbed earth. That scares the bjeepers out of me, though. I vote to leave this one to the guys who are already equipped for it and have estensive experience at it.