Color overlay on objects without affecting the material

I update this post to see if I can get any help…
The idea would be to “add” a color overlay on a given object without affecting it’s material… if this is even possible…?

New update: problem solved!
I managed to get what I needed (a single material, which looks different from one object to another in terms of color and transparency).
For this I used the “Object Info” node in the Blender material definition (see here).
The “Color” output controls the color of the overlay, and the “alpha” output controls the overall opacity of the material.
Be careful if you use normal maps in your material to make sure that the normals are correctly computed (if they exist at all!) for the objects to which the material is affected. Otherwise you may experience unexpected render issues (see here to force the tangent computation on your geometry if this attribute does not exist)… I struggled to find this one!!

Hi Kdv! I did not see your post when I found the same solution. Anyway thanks a lot for the help and the illustration
Cheers

David