Motivated by the increasing design for test (DFT) area overhead and potential performance degradation caused by wrapping all the embedded cores for modular system-on-a-chip (SOC) testing, this paper proposes a solution for reducing the number of wrapper boundary register (WBR) cells. By utilizing the functional interconnect topology and the WBRs of the surrounding cores to transfer test stimuli and responses, the WBRs of some cores can be removed without affecting the testability of the SOC. We denote the cores without WBRs as light-wrapped cores and present a new modular SOC test architecture for concurrently testing both the wrapped and the light-wrapped logic cores. Since the WBRs of cores that transfer test stimuli and test responses for light-wrapped cores become shared resources during test, conflicts arise during test scheduling that will negatively impact the test application time. As a consequence, to alleviate this problem, we present a novel test access mechanism (TAM) design algorithm for the proposed SOC test architecture. We conduct experiments on several SOC benchmark circuits and demonstrate that, with an acceptable increase in test application time, the number of WBRs can be significantly decreased. This will ultimately lessen the necessary DFT area for modular SOC testing and reduce the propagation delays between cores.