We explore the use of a switchable single-photon detector (SPD) array scheme to reduce the effect of a detector s deadtime for a multi-bit/photon quantum link. The case of data encoding using M possible orbital-angular-momentum (OAM) states is specifically studied in this paper. Our method uses N SPDs with a controllable M x N optical switch and we use a Monte Carlo-based method to simulate the quantum detection process. The simulation results show that with the use of the switchable SPD array, the detection system can allow a higher incident photon rate than what might otherwise be limited by detectors deadtime. For the case of M = 4, N = 20, a 50-ns deadtime for the individual SPDs, an average photon number per pulse of 0.1, and under the limit that at most 10 % of the photon-containing pulses are missed, the switchable SPD array will allow an incident photon rate of 2250 million counts/s (Mcts/s). This is 25 times the 90 Mcts/s incident photon rate that a non-switchable, 4-SPD array will allow. The increase in incident photon rate is more than the 5 times increase, which is the simple increase in the number of SPDs and the number of OAM encoding states (e.g., NAM = 20/4).