Does the Playstation 4 Support a 10TB hard drive?

Since the latest firmware update 4.50 the use of external hard drives is supported, though 8TB is the largest supported size.

Most models support an internal hard drive up to 4TB and unless you find a 2.5 inch one, you'll be stuck using a Data Bank (Nyko) like Timmy Jim described. The use of a data bank for 3.5 inch hard drives used to disable your stand-by mode.

If you wanted to test a 10TB hard drive (if you have one already) your safest bet would be to format it correctly and attach it like an external hard drive after you update to firmware 4.50.

To answer your main question, I've found an article that says certain models can support up to an 8TB hard drive.

PlayStation 4s with a model number below CUH-1200 can accommodate drives up to 4TB in capacity, while PS4s with a model number above CUH-1200 can handle up to 8TB.

However, you'd be hard pressed to find an 8TB hard drive that is 2.5 inches. You can use something called a Nyko Data Bank which will allow you to use 3.5 inch drives, but it's essentially an external hard drive closure, and will add to the size of your PS4 (not a big deal, unless your PS4 is in a small space).

From the page I found, I don't think a 10TB drive will be supported. Realistically, 8TB should be more than enough (it would be for me!). The article also noted that a 6TB hard drive would be more preferred from a cost perspective, but if cost isn't a factor then there are certainly some 8TB options available.

I can confirm that 3.5 inch 10TB HDD (I tried Seagate) & 12TB HDD both work in external and internal modes without any problem.