From my point of view, you have two basic options:
(1) Use a voltage reference provided by the DUT. This implies, that your DUT is self-powered or has a power input stage which can be feed from the programmer.
(2) Provide the voltage reference to the DUT. This implies, that you can change the voltage via HMI (DIP Switches) or Software. It also implies, that you frie your DUT in case of incorrect settings.
(1):
Provide a single Pin in your interface connector for VRef - per VRef (if multiple Banks). Connect this pin to the IO-Voltage required on the DUT. On the programmer side use a power op-amp with safety circuits ( overcurrent- , overshoot-, undershoot- , ringing- etc. protection). Drive the DUT-VCC of a common level-shifter IC.
(2):
Use a MCU with internal DAC to feed the output voltage into a voltage-controlled LDO. Power the DUT and the level shifters with this rail. You can do this with multiple banks on different voltages as well.
Think about a way - i can come up with none - to prevent a user error from frying your DUT.