The MUX Shield has three 16-way multiplexers (not shift registers). The multiplexers act as selector switches. You put an address from 0 to 15 on pins 2,3,4,and 5 and read from the three multiplexers on pins A0, A1, and A2.
You can't just stack the MUX Shield to get another 48 inputs but you can share the address pins (2-5) and hook the multiplexers to other analog pins (like A3, A4, and A5) for reading.
Because the multiplexers are two-way switches you CAN use them for outputs but you can only do HIGH/LOW outputs (not PWM) and you can only output to the three pins referenced by the address. If you change any of the address pins your three outputs now show up on different MUX Shield pins. (Not very practical).