Today’s invention is a monorail train which makes use of existing track.
This would have rollers, to fit either side of the rail and probably be gyro-stabilised (it worked in 1909, so the technology is proven).
This would provide for vehicles with much lower drag (being somewhere around half as wide as conventional trains, based on the wagon designs of prehistory).
The main benefit would be that it effectively doubles the amount of track available.
Since trains can be increased in length, with only a small penalty when loading at platforms of current size, this offers both a huge increase in the capacity of a rail network as well as allowing the vehicles to move more rapidly and provide passengers with a less restricted view.
Points switching would need to be timed, so that two trains could avoid a simultaneous change in direction which was not required.