In a multi-stage torsional coupling and associated methods of providing variable stiffness, the coupling has an inner member connected to a first torsional connection, a sprocket plate connected to the inner member, one or more plates connected to a second torsional connection, an outer member rigidly attached to the one or more plates, and a plurality of damping stages arranged for sequential engagement by movement of the sprocket plate relative to the one or more plates to provide a variable stiffness over a angle of angular displacement for the multi-stage torsional coupling. The sprocket plate is rotatable relative to the one or more plates to sequentially engage the plurality of damping stages to provide stiffness between the first and second torsional connections that increases in a non-linear, or stepped, manner as the amplitude of the angular displacement of the sprocket plate relative to the one or more plates increases.