Battery monitor on ADG507 and AD7705
Here's the problem as I see it: -



When you have the battery system going through the multiplexer because there is no galvanic connection to a reference on the measurement side, the differential output from the mux will be the battery voltage but it could be "lifted" with a common-mode voltage up to maybe 12 volts (for instance). So the diff voltage is fine but it is highly likely that the input to the ADC will far exceed its range of GND to Vdd - read the data sheet on page 5 and look for 


  Absolute/Common-Mode AIN Voltage