I use a roasting rack upside down, it holds 6 racks of trimmed ribs. I have to bend them in a little on the sides if the racks are long.
I have only done 6 at anytime but i image with another rack I could do 12 at a time, but I do like to lay them flat once I foil them so with more than 6 they would need to be on top of one another. I can only fit 3 ribs per grate flat.