Thank you for your post and welcome to the forums.
We have tested up to 1TB HDD formatted NTFS. The BDP-S590 recognized the HDD and was able to play back the media files. FAT32 should work also. You would have to verify if the 2TB HDD can be recognized by the unit.
As suggested by Nathaniel, you can use a hard drive formatted with FAT32 file system.
NTFS-formatted hard drives are compatible and can be recognized. However, the hard drive should have its own power source; the Blu-ray Disc (BD) player may not be able to power a stand-alone hard drive through the USB connection.
NOTE: The BD player will not recognize external hard drives formatted in MAC computers to be used for Time Machine Backup feature. In this case, the hard drive must be formatted and all of the existing partitions must be deleted for the drive to be detected.
If my post answers your question, please mark it as an "Accepted Solution."
I use Western Digital 3TB My Drives, Formatted NTFS and they work perfect on the Sony BDP-S3100 and PS3. However I think its odd that the Blue Ray player and the PS3 (assuming the PS4 is the same) use a UFC2 partition (same as Linux) but will not see a External HDD formatted to UFC/UFC2 or EXT3/EXT4. Not everyone uses Windows. Every machine I have ever bought is either MAC or has Linux. Really wish Sony would look outside the box and not conform to what everyone else does.