In the Mill, the columns had either two or four wheels per cage (depending on the version, but later designs had two). They were equivalent, and microcode typically had to keep track of which set held the value at any given time. Then in principle it's possible to make any transfer non destructive by simply grabbing a copy on the alternate set of wheels. This is what makes the split communicating state machine control in the mill so ingenious. Without it, when multiple axes are involved, there would be a combinatorial explosion on keeping track of everything.

Although axes in the store had two wheels per cage, the situation there is different, as the two sets were considered distinct variables selected by the cards. Babbage just used this as a way to reduce by half the number of columns needed for a given number of variables.

– Tim