We examine the role of mobile rings on the stretching profile of a single polyrotaxane molecule that is tethered in space by fixing one of the rings, the "control ring'. We show that the translational entropy of the mobile rings can lead to dramatic changes in the response of the chain at small applied forces. In particular, if the mobile rings are placed asymmetrically about the control ring, the chain can be very stiff at low force, displaying a yield force below which chain extension is minimal. However, at large forces, the entropy of the chain dominates the response of the polyrotaxane, and the effect of the mobile rings is negligible. These predictions of a stiffer polyrotaxane chain with added mobile rings might have implications in the design of polyrotaxane gels.