We present a scheme for a photon-counting detection system that can be operated at incident photon rates higher than otherwise possible by suppressing the effects of detector deadtime. The method uses an array of N detectors and a 1-by-N optical switch with a control circuit to direct input light to live detectors. Our calculations and models highlight the advantages of the technique. In particular, using this scheme, a group of N detectors provides an improvement in operation rate that can exceed the improvement that would be obtained by a single detector with deadtime reduced by 1/N, even if it were feasible to produce a single detector with such a large improvement in deadtime. We model the system for continuous and pulsed light sources, both of which are important for quantum metrology and quantum key distribution applications.