But if the paper can't be assumed to be white, CMY need to be opaque, otherwise yellow on black paper would just look black. Then you can no longer create red, green and blue. So you need additional red, green and blue pigment, likewise opaque. So "CMYRGBKW". Then the other colors can be mixed via dithering the eight base colors as usual.
Or maybe your printer still needs white paper, and the white pigment has some other use?