I participated in a thread at http://www.videohelp.com about a similar question. My suggestions there apply here.
Stay away from drives in an external case* from Seagate and WD because the cases are cheap (external drives sell for less than internals because the the cases are cheap) and are prone to the USB connection dying prematurely.
External drives in LaCie, Fantom and a few others are fine since they’re premium cases with internal drives.
*If you’re willing to open the case and possibly void the warranty (which can be as little a one year anyway) to remove the drive (which are identical to those sold separately) to use as an internal, they are the greatest bargains currently available. More about this below.
Unless you really need the spanning and redundancy of Raid, get a multi-drive external HDD enclosure like a Mediasonic Probox which are available in 4 & 8 bay configurations that have USB 3.0 and eSata connections with RAID capability for a bit more. They’re definitely compatible with 10TB drives (I have a couple of 10TB drives in mine) and there’s no reason they wouldn’t work with larger drives also.
Note that all prices are U.S. as of May 2018
I have 10’s of TBs of HHDs and buy new drives based on price per TB with Seagate and WD 8TB external drives (that you’ll remove the drives from ) are the sweet spot for price per TB @ ~$20/TB (<$160 per drive). 8TB & 10TB internal drives are ~$30/TB and 12TB drives are ~$35/TB
A 4 bay Mediasonic Probox is ~$100 and the 8 bay model $250 (I have both) and they work identically.
For <$1000, you can get five 8TB externals (40TB storage) + a 4 bay Probox or three 10TB internal (30TB storage) + a 4 bay Probox that you can swap drives in and out of.
You state your files are ~4TB, so if they’re 4TB or less, you can store two files on an 8TB drive. If they’re between 4 and 5TB, go with the 10TB drives.
I’m not sure if this still applies, but the real bargain through the end of last year was that all WD 8TB externals contained WD Red NAS drives that retailed as internals for twice the price. Yes, you risk voiding the warranty by opening the case (that is extremely easy to do without breaking any tabs), but you get a high quality drive for half the price. Knock wood I haven’t had to do this yet, but I’ve read that WD may honor the warranty on an opened external drive (replace the drive back into the case) since the warranty is is on the drive itself, not the case/drive combo.