A method is provided for using low-overhead equipment to construct a deep piling foundation for an existing building. The method involves lifting the existing building to a predetermined elevation above grade and positioning cribbing stacks to support the existing building at the predetermined elevation above grade. The cribbing stacks are spaced from each other enabling low-overhead equipment to maneuver underneath the elevated building to drill drive pipe piles at designated locations to provide optimal support for the building. Grout is pumped under pressure into the pipe piles continuously during the drill driving of the pipe piles so that grout exits through a grout port to mix with disturbed soil about the pipe pile to encase the pipe pile in a grout-soil mixture. Pile caps are attached to each pipe pile and secured to the existing building so that the existing building is supported by an array of the deeply driven pipe piles which serve as the foundation for the building.