The 2nd tower at Starbase is much more modular than the first and is being built at quite a rapid rate.
They’re building one at the Cape, too, but they’re still a multi-month process.
Construct additional pylons?
Why not to use the Mechazilla for adding the next section of tower on top of existing one? So we transport parts to the tower, assemble relatively thin sections of tower nearby, the lifter moving along the tower brings the sections on top of existing ones, and we have a few places for optimizations here. The proponents of The Boring Company may see some parallels here.