I've worked out one that "can" be built (it's beyond ridiculous, though.)
Build towers around the equator. Build a ring around the equator on those towers. Build a ring inside the ring, maglev supports. Evacuate the ring, spin the inner ring above orbital velocity. The objective is to generate as much outward force as the weight of the entire assembly including the towers.
Do it again, on top of the first one. Keep doing it until you reach synchronous orbit. If you want to go higher the inner ring is not moving, exerting downward force countering the outward force of the rest of it being above orbital velocity.
Forces:
1) Compression on the towers. Note that this goes to zero as tower height goes to zero.
2) The outward force on the ring exists across the whole ring, but the downward force of supporting the towers only exists where there is a tower. Your ring needs to be stiff enough to counter this. But, again, note that this force goes to zero as the space between towers goes to zero.
3) Maintaining a very hard vacuum in the structure.
We know how to do #3, the others must have answers. Thus it can be built.
Nothing else is feasible with current technology, the taper of the cables is highly dependent on the strength of the material (in tension, an elevator is based on always pulling out as the upper end isn't hooked to anything.) You need much better than anything we can currently do before the taper blows up so badly you can't build it.