Hi Andrzej,
I don’t know if it is possible to control the GI for each material individually, as I know that this is done through the render setting. Still, if what you are looking for is to increase the emission while avoiding bleaching, you can copy your model and use the second copy as an emission source, regardless of how much it will turn into The white color. After that, you could use Compositing tag to hide it only from the camera and keep the rest of the effects, including the GI, Therefore, you will have two models, one through which you control the appearance and a hidden second through which you control the amount of emission.
I hope this helps you.