I can't pretend I understand the scenario you are painting in your question but here's a brief explanation of how common mode rejection works. Look at the picture below - it shows both inputs connected to an AC signal that represents the common mode voltage: -
There is no real wanted signal just the unwanted common mode voltage. OK so far?
Think about Q1 first. If its base voltage rises a little bit then so does its emitter - this is natural transistor action and applies to MOSFETs or JFETs too. The effect of the emitter rising (common to both transistors) is that Q2's emitter rises and, because its base has also risen, there is very little net increase in base current into Q2 (or Q1).
The lack of change in base current for a significant change in the common-mode base voltage means very little change in either transistor's collector current. Very little change in collector current means very little change in collector voltage.
Hence, an identical significant change in base voltage on BOTH transistors results in very little change in collector voltage. This is the beginnings of largely rejecting a common mode (interfering) signal.
Simple statement: The gain of a differential pair amplifier to a common mode signal is significantly smaller than its gain when presented with a differential signal.
However, given that there is actually a small change in collector voltage for a significant change in common-mode base voltage, it is useful to note that both collectors will rise and fall together due to this significant common mode input voltage. This is very important because if a differential signal is applied the collectors go in opposite directions.
So, if the collectors were then fed as "a pair" to another set of differential inputs, common-mode signal rejection (in this 2nd pair) would be increased as a square term. In other words, if the first stage reduced common mode voltages by 10, the 2nd stage would reduce the common mode voltage by 100.
EDIT to cover the question about common-mode range exceeding power supply: -
Here is the equivalent circuit of the A and B inputs to a RS485 transceiver (SN65HVD485E): -
Note the external input is attenuated because of the 180 kohm and the two 36 kohm resistors and, although the device runs from 5V, it can handle input common mode voltages (absolute maximum ratings) of -9V to +14V.