But to be a space elevator replacement you would need a tower that could bear load up to geosynchronous orbit. That's not what I'm suggesting. Build the tower

But to be a space elevator replacement you would need a tower that could bear load up to geosynchronous orbit. That's not what I'm suggesting. Build the tower as high as is practical, say 100 km. Then launch your space elevator satellite and lower the cable down to the top of the tower. The cable has to support its own weight, so it has to be thicker at the top than at the bottom. It turns out that the cable thickness has to taper exponentially (basically, this amounts to a rotation of the catenary problem). So not having to support the last 100 km of cable at the end translates into a weight savings along its entire length.