A Uno actually has 14 digital input pins, but only 6 analog pins. If you are actually trying to interface pots, then yes you would need to multiplex some of the analog ports, however your drawing (such as it is) shows rotary encoders which are digital (and not pots). So the place to start is likely tell us what is actually there ... Assuming you are trying to multiplex analog signals your mechanical switch could be replaced by an analog switch IC letting the software operate the switch for you.
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