For large-scale modal analysis problems, Component Mode Synthesis (CMS) methods are very attractive, as they reduce the global problem into smaller subproblems on substructures. However, the substructure bases do not span the desired solution space efficiently, thus the error decreases slowly as the number of substructure eigenmodes increases. We demonstrate that a much more effective subspace can be constructed by combining substructure eigenmodes from multiple spatially staggered partitions of the input domain. To further accelerate the method, we replace the bases on the substructure interfaces by low-frequency approximations excited from the substructure eigenmodes from other partitions. Compared with typical CMS methods, our approach improves the accuracy by 3 orders of magnitude and achieves better strong and weak scaling in both time and memory cost. The advantages inherited from CMS, i.e. fast local updating and low communication cost between Message Passing Interface (MPI) ranks in large-scale distributed computing clusters are verified as well.