CDR Robot Backup solution

I think the closest you might come is a device used more for in house automated cd-r duplication/production. So they work more like sending it an image and how many copies needed, and it burns them. That would probobly be fine for a back up situation, but the "We want to give them the ability to bypass the quota of there disk" line in your post leads me to think it's not just back ups. Not sure if they can be set up to to do what you need, but search the web for a manufacturer and ask. Note most of these also have printers to print on the label side of a disk.

You might also want to consider that these types of set ups cost several thousand, that's enough to buy about a TB of HD space.