Yes, you can pour a foundation under an existing house. This is called underpinning, and it's done when the original foundation is no longer level or stable. Underpinning involves excavating around the perimeter of the house and pouring new footings and foundation walls. The new foundation is connected to the existing foundation with reinforced steel rods, and concrete is used to fill in any gaps. Once the new foundation is in place, the house is lifted up and resting on top of it.