Well I'm pretty sure that the 4TB hard drive that you have in mind will be a 3.5 Inch drive which makes things a little bit more complicated. The PS4 has a built in slot to insert any 2.5 Inch hard but 2.5 Inch hard drives are more expensive and don't have as high of available capacities. A 3.5 Inch hard drive will not fit in the slot that the PS4 has available. Earlier this year Nyko announced that they are making an adapter for the PS4 that allows the usage of 3.5 Inch hard drives but that will make the console more bulky and the adapter is rumored to cost about $35-40 on top of the cost of the hard drive itself.