Keeping an enterprise-worth of files up to date is probably best done the way that sync clients keep an individual user up to date: After an initial export, use the /events API to capture all the file-ids that change for the enterprise, and re-download them when it makes sense to.
If you want to do this, depending on how large of an enterprise you have, you will likely hit rate limits. You should reach out to Box to work with them on getting higher rate limits. Tuning your own algorithm and minimizing how often you do a download will most likely be key to keeping your solution working optimally.