Store multiple versions of large binary file with minimal data duplication (preferably Linux)

ZFS on Linux with deduplication may be your friend in this case. There are Red Hat RPMs/repos available for installation.

Even without dedupe, if you can work this into the ZFS snapshotting workflow, there are some significant advantages to attempting this with ZFS.

Can you explain a bit more about how you wish to work with these files? Are you seeking point-in-time snapshots, or copying multiple revisions of the same/similar files to the datastore?