When my brother had a house in Salt Lake City, he had a basement dug under his house. They dug a ramp under the exterior wall with a skid steer, braced up the concrete footing, then just kept driving that skid steer farther and farther under his house until they got all the dirt out of there they needed to. The rest of the house was still undisturbed and when they where done digging, they braced everything up and poured concrete from the ground to the bottom of that exterior foundation wall. It all seemed pretty simple and straight forward to me, but I wasn't there, I just saw pics and talked to my brother while it was going on.
I'm planning on putting a storm shelter under the slab of an addition that I'm also planning on building. My plan is to start the stairs 2 feet from my existing exterior footing and go down from there. I'm not planning on doing anything special to support that wall while digging. I think that's far enough away that it wont affect anything.
Eddie