Custom EDID for specfic physical monitor, not output

I have a setup where I connect to two different displays depending on where I am. I would like to use a mode which one of the monitors doesn't allow, but that won't be loaded when any other display is connected. To be more concrete, the I would like to overclock the external display at home to 120hz, but not overclock a different display at work that I connect to the same HDMI port. Is this possible using nvidia? I can't seem to be able to override EDID with xrandr, at the same time using the EDID settings by default.