Sometimes we need to group a group. For example, for complex appearances, to nest graphics styles.
But Illustrator does not allow that — and in most cases it’s a proper cautious behavior. But perhaps it can be toggled somewhere?

So far we have two workarounds for this.
1. Create a dummy object, select both it and the group you want to 'wrap', group them together, delete the dummy object.
2. Use a script 'Add Group Anyway': https://onthehead.com/ais/group003/ (it also can pull children form different groups into a new one — which is a thing we want too).