Some interesting responses
I was thinking of Douglas Self's Power amplifier book. In some of the measurements he makes the distortion of his Audio precision system is plotted as a reference trace, to show that the distortion at some frequencies is almost entirely from the measurement system, rather than the DUT.
As pointed out, directly subtracting the THD figures could cause some errors. I wouldn't like to rely on the idea that all the distortion is only directly additive.
However, if it was done within the measurement system, it might be possible that phase could be accounted for, i.e. by using the complex output of the FFT, rather than by subtracting the magnitudes?