Stage-level reconfigurable chip multiprocessor (CMP) aims to achieve highly reliable and fault tolerant computing by using interwoven pipeline stages and on-chip interconnect for communicating with each other. The existing crossbar-switch based stage-level reconfigurable CMPs offer high reliability at the cost of significant area/power overheads. These overheads make realizing large CMPs prohibitive due to the area and power consumed by heavy interconnection networks. On other hand, area/ power-efficient architectures offer less reliability and inefficient stage-level resource utilization. In this paper, I propose a hierarchical multiplexing interconnection structure in lieu of crossbar interconnect to design area/power-efficient stage-level reconfigurable CMP. The proposed approach is able to keep the reliability offered by the crossbar-switch while reducing the area and power overheads. Experimental results show that the proposed approach reduces area by up to 21% and power by up to 32% when compared with the crossbar-switch based interconnection network.