Of course you can, that's why you use differential ones! And you'll need to feed it into an op-amp/instrumentation amp with CMRR higher than the total battery voltage. That's the standard way of doing it.
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I should have said max CM voltage rather than CMRR. Hope I didn't confuse anyone.
Here is an example of a differential multiplexer that can accept up to a 72V input. You'd need one for every 4 cells assuming that your battery voltage is within that limit. The output of the mux would go to an instrumentation amplifier that can also take a 72V input. This amp will take the difference between the two inputs, which will be the cell voltage, and safely feed that to the arduino input.
Not exactly a beginner project, but it is definitely doable if you take care and learn along the way.
This is a Chevrolet Volt battery. The black box on top is the BECM (Battery Energy Control Module). There are six plugs into it that monitor 16 cell groups. A cell group is two 3.7V Li-Ion cells in parallel. Each cell group is monitored by the BECM, and there are 96 different OBD codes (Check engine light). The cell groups are all wired in series giving a total of 355V.
Thanks Steve - interesting video. (I didnt watch all 2 hours)
I'd guess that a cell group in a battery must be replaceable, otherwise there is little point in monitoring each seperately.