How can I use a dual 4-channel analog multiplexer independently?
Sounds to me like you normally wouldn't use a multiplexer at all. Because there's no need for signal multiplexing – you just need to switch resistors in and out of your divider:







simulate this circuit &ndash; Schematic created using CircuitLab

How you implement the four switches depends on the supply voltage and on the magnitude of the resistors we're talking about – if R_sensor + R1…R4 is something like kΩ, and your supply voltage is let's say 9V, then, by all means, use a simple tri-state 8bit shift register to pull exactly one of the four R's outputs down, and leave the rest floating. Account for the voltage drop in the shift register.

If we're talking several Ω, implementing each SW with a low-r_dsOn MOSFET might be the better alternative. You could, again, easily control these directly with some IO pins, or with a shift register. BJTs might also be a good alternative.

Another pretty intuitive option: There's digitally controllable resistors. They work pretty well for low-frequency and DC applications. You can program them to have a specific resistance.

Yet another option: what you're actually doing by changing the R is changing the current through your sensing resistor. So why don't you simply build an adjustable current source? There's different ways of doing that, but if you need low component count and high accuracy: there's current-source DACs designed exactly for such measurement jobs.