I have seen such a thing as a 5 speed single phase 120 volt motor. I forget whether it was shaded pole or permanent split capacitor but it was for a furnace blower. Some of the speed taps were for adjustment for short or long ductwork systems.
I also know that some paddle fans use 3-speed motors. If you have a bunch of them you need to have individual relay contacts for each fan. In a cheap motor each speed tap could be off a winding turn or two. You could also hook the group to a big solid state controller but most people really only need 3 speeds.