I bought a Seagate 2TB slim drive to backup the 1TB drive I have had in my PS4 since the beginning.
Originally, the PS4 could not see the USB 3 drive because it came formatted as NTFS from the factory.
I connected the drive to my Mac and formatted as exFAT (since many files are likely larger than 4GB) but the PS4 claimed the drive did not have enough free space (in fact it claimed it had 0k free) even though copying individual games to the drive worked.
I resolved this issue by formatting with a partition format of Master Boot Record. The default for Disk Utility on the Mac is GUID partition format, which appears to not be compatible with the PS4.