[Jared Russell]

I have often heard that cascaded elevators require a return drum of a different diameter than the feed. But wouldn't the following work?

Each segment of the elevator can have a closed loop of belt/chain attaching it to the prior stage. It should be anchored at the top of the previous stage (or motor for the first stage), and the bottom of the next stage. It's important that the total length of the loop doesn't change as it travels up and down.

You still have the speed and force multiplier effect with each stage, but you won't have to worry different feed and return speeds.