At the cost of memory, Im quite shocked that they are resisting getting more. You can get a 5 TB for roughly $140 at Costco nowadays. We use a set of 16 TB Buffalo Terstations. Our entire office works directly off on one, and it backs itself up to another every weekend just in case something happens. I archive these to coldline every couple months in case of a major disaster. We also archive products every couple months to a set of 5 TB drives that are unplugged and rarely used (only exist to help alleviate space issues on the 16 TB). My industry is a bit different in that we really only need the files associated with the final output, so I make sure all iterative files, preview images, and general junk is cleaned out at the conclusion of a project.
That being said, I work at a 3d rendering and animation firm that relies completely on digital assets. We of course output massive amounts of data. I dont know your exact position, but you may really want to look into a NAS drive that allows for RAID backup. Drobo, synology, and QNAP are all business class. The Bays will cost roughly $500, but then you can add in the size of drives that you feel is appropriate. Just remember to use RAID, as the extra cost now will easily pay for itself when the drive inevitably fails at some point.