If a Raw image file is made with mixed lighting, - multiple light sources having more than 1 color temperature - white balance can be accurately set for only 1 of the color temperatures.
White balance can only be partially corrected for each of 2 or more color temperatures.
As an example, a scene shot in a room that has both fluorescent and tungsten lighting can be partially corrected for both or fully corrected individually.
If one color temperature is fully corrected, the image will still have a color cast from the other color temperature. If both are partially corrected, the image will have a lesser color cast from both light sources.
In a case where fluorescent and tungsten light are present, a filter can be put on the lens to correct for one or the other light source, and the camera can then be set to the white balance of the not filtered light source.
In a situation where fluorescent light, tungsten light, and a flash are used, there would be 3 color temperatures of light. In that case a gel can be placed on the flash to make it's light match, say the tungsten light, in the scene, a filter would be put on the lens that corrects tungsten light, which then allows setting the white balance in the camera, or correcting the white balance post process, to fluorescent.