Is offloading the data to a NAS a possibility? If you're just looking for a case that integrates that function, the Silverstone DS380B lets you put in loads of 3.5" drives along with a working system and SFX PSU. But it's not ultra-small.
I'd want to buy that case just for that little power supply.
Aibohphobia, you right, sorry for my mistake (
I told about prototyping in 2015, but in 2016 this case made with aluminium:
BTW, this case goes with built-in CPU cooling system and built-in PSU
I'd want to buy that case just for that little power supply.