(remember that this wall was for existing so iI haven't bothered with a cavity etc).
But when I apply the modifer to the wall and select the 'sleeper' componant, it comes alive and takes on the new material assigned.
You can of course have the added portion as a separate entity instead but this way, the material is controlled from & by the wall style which is logical because it's part of the wall. It moves with the wall.
The other big advantage is that you haven't created another wall style to have to maintain, keeping things simple. If you alter the wall style, this one wall won't be left out. On the General tab of the wall style, you may want to add an explanation just in case someone else works on the file.
Hopefully that's made it a bit clearer but I have at least one other example I will post that also can utilise the 'sleeper' componant.