You can multiplex rotary encoders very easily using diodes (I'm looking at a unit with 3 muiltiplexed rotary encoders as I write this):
- connect the common terminals of the encoders to Arduino output pins (1 output pin each, so 5 pins)
- connect the left encoder terminals to a single input pin, each through its own 1N4148 or similar diode (cathode to encoder, anode to input)
- ditto for the right encoder terminals, using a different input pin
- ditto for the pushbutton terminals, if you are using encoders with built-in pushbuttons (connect the other side of the pushbutton to the common terminal).
You can share the 5 output pins with other multiplexed devices such as 7-segment LEDs. You pull one of the output pins low at a time, then read the 2 input pins to determine the state of the selected encoder. Enable the pullup resistors on the input pins.