Temple: Simultaneous sharing with Family Group and Temple System

I think that the functionality of the Family Group feature for temple reservations could be improved if reservations could be shared with both the family group and the temple system.
I have thousands of names shared with the temple system, but I also have a (small) family group that I share names with. I have too many names for my family group to possibly be able to do all of them, but I would like to have as many names as possible available for my group to reserve if they want.
Would it be possible to allow names to be shared with both the temple and a family group? Essentially, the name would be visible to the group and they could reserve and complete it, but if the temple system gets to it first, it will still be taken from there and completed.
Does this sound like a useful and feasible idea?