Well, at least based on what you show there, it would be much faster to start over and model it the way the client wants it done. It would be interesting to know exactly why the client thinks they need the edges and faces to be tagged. That goes against the normal rules for modeling in SketchUp. From what little information you’ve actually provided about the project, I’m inclined to think they don’t properly understand the use of tags in Sketchup.
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Why groups? As there is a lot of repetition, shouldn’t you be using components instead? With components, any edit you do is reflected to all its copies.
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Yes you can, in a faster way.!
I was looking for the same thing (forget about all those questions “Why…???”) - if you want it, then it must be a good reason, those that seek especially for something like this are not beginners.
There is an extension in Sketchucation called “PutOnLayer”, there are a few versions of it, and one of them does exactly that in a single operation - putting everything you selected (nested or not, including geometry) on a tag of your choice.