Abstract: It was shown in current literatures that the performance of a dry friction damper would significantly change while the excitation level varies. This phenomenon originates from the non-linear nature of friction, and as a consequence, there is only one most suitable excitation level for an individual dry friction interface. The present work is devoted to extend the working range of a dry friction system with respect to the excitation level, by introducing multiple dry friction interfaces into the host structure. The torsional vibration of the host structure is considered, modeled by the Lumped Parameter approach and the Coulomb assumption. Firstly, the feasibility of such a system is discussed based on the derived non-dimensional dynamic equations. Secondly, an enhanced time/frequency alternating method is proposed, with a full consideration of the relative motions which could possibly happen in each dry friction interface. It is proved through a numerical integration method, that the proposed method is a precise and rapid tool for the solution of nonlinear systems in a frequency domain. The dynamic behavior of such a system was investigated via several groups of parameters, including the number of dry friction interfaces, the critical frictional forces and damper mass and etc. At last, the damping characteristics of a 2-interface system and a 3-interface system are presented respectively, showing the procedure of designing such a system.