If the idea is that you want to control all three of the parent tracks while they control the child tracks then your idea of a grandparent should work. Just create an empty track above the other three sets and make it the 'super parent' so to speak.
so long as you make sure to use the parent motion button to the left of the track rather than the track motion of the parent track (in the normal track motion location).
and there are some issues when parenting multiple layers that I've run into where it requires dual parent tracks to make it really affect *all* the child tracks.
I've seen some really cool things done w/ Parent/Child tracks that I thought were done in After Effects.
As I've never used Parent/Child tracks... I'm curious to see what you're doing.
Can you post a clip of the section?