I think you'll need to work out how to use additive blending. I can't really help you there, I haven't used XNA for a couple of years, Im using SlimDX and SharpDX these days. But if there is some restriction on using a blend state, then you'll have to get around that restriction. Because blending is definitely the method you need to use. Otherwise, how can you add one light to another ?
Edit : BindFlags = BindFlags.RenderTarget | BindFlags.ShaderResource ..... just sets a texture to be used as both a rendertarget and shader resource, so both input and output,
so a texture can be written to and then used in the next pass as a source texture.