We study a shared-memory center-stage switch with input multiplexers and output demultiplexers, where backpressure is applied from the demultiplexers to the center stage, and from the center stage to the multiplexers. We consider three backpressure schemes: (i) non-selective backpressure (NSB), where a congested center stage or a congested demultiplexer applies backpressure indiscriminately to all the traffic destined to it, regardless of the destination; (ii) per-port selective backpressure (PPSB), where the center stage applies backpressure selectively only to the traffic destined to the center-stage port(s) experiencing congestion, but a demultiplexer applies backpressure indiscriminately to all the traffic destined to it; and (iii) per-subport selective backpressure (PSSB), where both center-stage switch and demultiplexers apply backpressure selectively only to the traffic destined to the output link(s) experiencing congestion. We show that NSB introduces heavy HOL blocking which limits the throughput of the system and causes heavy losses. On the contrary, PPSB and PSSB achieve high throughputs, and allow one to increase buffer utilization in the system while keeping the majority of the buffers physically separate in the input multiplexers. Both these schemes perform very well in the case where only limited sharing of the buffers in the center stage is allowed, as required to guarantee fairness in the switch. With PSSB, small buffer sizes in the demultiplexers can be used. If the buffers in the demultiplexers are large, PPSB and PSSB offer comparable performance.