Just build it around a space elevator.
Dr. Robert Forward of Hughes Research developed the concept of dynamic support to build large structures. A linear magnetic accelerator acting upon a stream of mass provides a force-counterforce arrangement, along Newton’s motion law. This applies whether adding or subtracting velocity to the mass flow, the direction of the reaction force flipping positive or negative.
This provides for a circumvention of materials strength requirements. A structure can be built in which support is supplied along distributed points, by adding or subtracting momentum of a high velocity matter flow by electromagnetic manipulation. Obviously, electrical energy can be stored or extracted from the kinetic energy of a ferromagnetic mass flow. This exchange inherently involves the application of force to accomplish the transformation of one for another.
Yes! And don’t bother with the lower floors. Just the low orbit platform. Go big of FU.