Setting Tag Group's parent to another Tag Group?

Not really.

Tags already allow you to only allow a tag group to be used in certain categories, and you can also only allow a group to be used if the parent tag has been added.

I’m just suggesting that the parent function be extended to multiple parents by way of a tag group.

Only expose ‘this tag group’ if ‘any one of these tags (defined by a group)’ is already present.