Critical responses are frequently detected at the coupled torsional beam axle (CTBA) of a lightweight vehicle. However, the freedom to modify the design of the axle shaft is limited because the suspension system must satisfy other vehicle requirements such as steering performance. Conventional sensitivity analysis cannot provide practical information about the resonant behavior because the analysis only identifies the contribution of the axle shaft to the behavior. This paper presents a novel sensitivity analysis based on transmissibility ratios (TRs). The vehicle components other than the axle shaft that can be modified to control the critical spectra are identified using acceleration responses. A multi-body vehicle model is constructed to simulate the proposed design modifications, and the simulation results show that the vibration of the axle shaft is considerably reduced by the modifications. Because the TRs on the CTBA are effectively minimized through the modified design strategy, the resonant response from the axle shaft can be controlled efficiently.