I see more clearly now what you are trying to do, having looked at your model and the Dynamic Attributes.
You want to be able to select a light shade of colour for the outer component Container Short, and a darker shade of the same colour for the two inner (ContainerShades) components, using one drop down selector in Component Options.
So you have at least 8 materials - four colours each in two shades: light and dark.
If you want to be able to edit all ‘similar’ components for size, but keep the colours different, I don’t think you can do it the way you are trying to, for the reasons I outlined in my original post.
I’m wondering though, if you put a third component, permanently coloured black, behind the ‘shades’ components, and made them partly transparent but of the same colour as the outer component, whether the black behind transparent would show as a darker shade?
Let me try that, and get back to you.
Well, I have the basis of a solution.
I’ve duplicated the ContainerShades component, made one unique, and coloured the faces of the copy a 50% transparent gray, and put it 10mm in front of the original ContainerShades (so as to avoid Z-fighting). Then moved the pair back 10mm so the front (transparent grey) is flush with the outer container shell, and mirrored the pair to the back of the outer container. (By the way, the back face of your outer container was reversed, with the inside out. I fixed it).
You can now apply different colours using the paint bucket to the whole component, to get this appearance.
Four instances of one component.
Container.skp (69.5 KB)
Does this give the look you wanted?
Now if you want, add dynamic attributes to change the sizes of the containers.
And if you want the shaded panels to look more ‘solidly recessed’ you could extend the coloured back to include sides up to the front, and/or increase the separation of the two copies. As they are, you get an impression of recessed panel, but up close you can see the gap.
I’m not at all sure what would happen if you try to make the colour a dynamic option now - it would probably still create a new component definition for each colour, but it’s after midnight here in UK, and I’m off to bed.