In general, hallways can be reinforced to with stand EF3s. Beyond that, I am not certain that the capability exists.
I live in Missouri, and one of our local businesses was exploring how to do this since they weren't able to get a basement. The construction companies were willing to bid up to EF3. Not sure why - Maybe the technology is iffy for such a large area, or maybe a liability issue for the company/architect.
Maybe they are, but a tornado shelter isn't that big, and if your family's life were to depend on it, expense is probably a secondary consideration.
If they are only talking about sandstone, which you can break through with a crowbar, I've seen them drill and blast granite out here in various construction projects. Granite is as hard, or harder than commercial concrete.
You can rent an electric jack hammer. One of those, some beer and a few guys with shovels could probably make an 8x8 or appropriately sized hole in half a day.
The rest is traditional concrete/rebar construction. Put in an air vent and a sump pump. The whole thing wouldn't have to be below grade, you could berm up dirt over it. Might want to check it periodically for rattlesnakes.
During the reporting, I saw a couple of doors into the ground where people had survived this twister, so it is possible.
Judging by the fact that pieces of heavy debris had been moved long distances, they are now considering upgrading the storm's rating to an E5.