For what we believe is the first time, the feasibility of large-port-count nanosecond-reconfiguration-time optical switches is demonstrated using a hybrid approach, where Mach-Zehnder interferometric (MZI) switches provide low-loss, high-speed routing with short semiconductor optical amplifiers (SOAs) being integrated to enhance extinction. By repeatedly passing signals through a monolithic hybrid dilated 2×2 switch module in a recirculating loop, the potential performance of high-port-count switches using the hybrid approach is demonstrated. Experimentally, a single pass switch penalty of only 0.1 dB is demonstrated for the 2×2 module, while even after seven passes through the switch, equivalent to a 128×128 router, a penalty of only 2.4 dB is recorded at a data rate of 10 Gb/s.