Prevent light combining with other lights

I tried to search for this but can't find much in terms of solution. Basically I have the following:

This is a picture of how the lighting looks like when the player (white circle) is away from the red light. The player has a intensity 7 point light, where the red light is a spot light with intensity 8.

When the player moves to the red light, the red light turns significantly lighter, and I suspect that it is due to the white light mixing with the red light, making it pink/lighter.

Basically I was wondering if there is a way to prevent them from mixing.