Assigning materials to multiple GP layers


I’m having difficulties assigning different materials to a bunch of GP layers. It seems to be “all or nothing” for Blender: it invariably gives the same material to every GP layer at the same time. If I change a material for some parts (while in Edit mode), it changes material for every GP layer all at once. And I don’t want any of that…

I need to have a material assigned to some GP layers and another separate material on some other GP layers: I can’t have just one material everywhere.

Can anybody help me with this GP tool ?

Thanks in advance.