Multiplexing of resistance measurements
Get a dual 3:1 analog multiplexor. (Or 4:1)

Wire the first 4:1 to each of the 4 resistors, with the common node to Current Source.

Wore the 2nd 4:1 also to each of the 4 resistors, with the common node to ADC Vin+.

Tie the ADC Vin- to "GND". I presume you can implement a 10 milliohm Ground connection between the 3 resistors. The value of 10milliOhm * 20mA is an error of 200 microVolts out of 0.16 volt, or error of 0.16/0.0002 = 1/800 or 0.125% error due to GND plane/GND wiring resistance.