Color calibration would not be the place to add this, as it doesn’t work with profiles at all. Instead it takes D65 input and applies a chromatic adaptation transform, which is, roughly speaking, a more accurate white balance. To what extent the CC algorithms relies on the input being D65, I don’t know, but it specifically always uses (how?) the standard matrix in input color profile “for consistency” even if another profile is chosen.
If dual illuminant (DI) profiles were to be supported, it would have to be in input color profile and probably white balance as well (if I understand things correctly).
Whether CC would benefit from DI profiles is an open question that I have yet to see an answer to, although some have suggested that it would (but without going into any detail how).
Have you tried creating custom WB coeffs, as described in this video?
That should at least get you consistent white balance output.
Do DI profiles actually provide enough correction to achieve that?
That seems to be specific to Sigma’s software and its quirks.
I actually proposed a possible solution, that would work with color calibration, in this thread: Create ICC or DCP Profile with costum linear Matrix
But I don’t think he ever made a feature request.