LightMask | A tiny 2D header-only flood-fill lighting engine | Game Engine library

To chain lights as you want, you need a different approach. As you already encountered, chaining lights solely on the color won't work, as once the color has become black it can't be highlighted anymore. To deal with multiple lights there are two typical approaches: forward shading and deferred shading. Each has its advantages and disadvantages, so you need to look which fits better your situation.

Forward Shading

This approach is the one you tested with stuffing all lighting computations in a single shading pass. You are adding all light intensities together to a final light intensity and then multiply it with the color.

Pros are the performance and simplicity, Cons are the limitation in the amount of lights and more complex shader code.

Deferred Shading

This approach decouples single lights from each other and can be used to draw scenes with very many lights. Each light needs the original scene color (albedo) to compute its part of the final image. Therefore you first render your scene without any lighting onto a texture (usually called color buffer or albedo buffer). Then you can render each light separately with multiplying it with the albedo and adding it to the final image. So even in the dark parts the original color comes back again with a light.

Pros are the cleaner structure and possibility to use a lot of lights, even with different shapes. Cons are the extra buffers and draw calls which have to be made.