Switching different loads without voltage drop
Forget it. Make rather a current sink with known and programmable load current and see how much the voltage drops.

Make a web search "voltage controlled current sink" You'll get several versions. Start from this EESE story: Help with trying to understand Voltage controlled current sources 

You can control it with DAC or PWM+Lowpass-filter from a computer. If you use PWM have also one I/O bit for fast force to zero. It has a transistor which shorts the low-pass filter output or otherwise makes the current=0 with no waiting the decay of the filtered control voltage.

The DAC can be external - a set of resistors connected with analog switches, no voltage drop problems, the resistors can be much bigger than the Ron of the switches.

If it must be switched load resistors for some invisible reason calculate or read from a prepared look-up table the correction which takes into the account the no-load voltage, the loaded voltage, which fets are ON and the measured properties of the fets.