Nonlinear energy sink (NES) systems, when applied to a physical system with multiple interference sources, exhibit abundant nonlinear dynamic behaviors. However, current research in this respect is limited within the theoretical scope of deterministic systems. According to the theory of cell mapping, this paper introduces a parallel restructured algorithm to improve the performance of cell mapping and cell processing, and a parallelized multidegrees-of-freedom (DOF) cell mapping (PMDCM) method is given. With the method, the global behavior of NES systems is analyzed so that the dynamical behavior of multiple stable attractors within typical parameter intervals can be captured. The research results show that for NES systems, there is the phenomenon of multiple stable attractors coexisting in multiple typical parameter intervals, which occurs between periodic and periodic attractor, periodic and quasi-periodic, periodic and chaotic attractor. While revealing the corresponding relationship between different types of attractors and their basin of attraction, these findings verify that the new cell mapping method has high computational efficiency and accuracy and can provide a theoretical basis for the study of high-dimensional nonlinear systems' global behavior and optimal control.