Eliminate Conflicting Light Sources
Right off the bat, you may be able to eliminate one or more of the conflicting light sources. In the room with daylight and fluorescent light mixed, for example, you may be able to close the curtains over the windows to eliminate the daylight. For a portrait with tungsten lights and window light, you can turn off the tungsten lamp and focus on using only the daylight. Your first step is to figure out what you can do to reduce the number of conflicting light sources. The fewer color temperatures you have to contend with, the better!
After you analyze the light in the room, you will be able to analyze which light sources you can eliminate. Also, if you identify the dominant light source in the scene, you can use that to your advantage by trying to eliminate any secondary sources of light.