Initially the idea stems from a ZDNet article By Jason Perlow in 2011 (link provided below) and some thought, the basics of a stackable computer would eventually be a personal blade server though without the bulk.
The device would consist of a base station similar to a NAS drive the design could either follow current NaS drive design trends or be stackable one module on top the other.
The Base station would house all the controlling hardware and management software, as in a blade server. It would effectively take control of all power management and storage solutions.
This is similar to a NaS drive though without the lag time as the internal network of the device would also consist of a SaN network for data storage.
The hardware is not the tricky part it is just costly for the design and initial set-up, there is currently a full rand of SoC (System on Chip) boards on the market with carrier boards, that would suit this project the modifications required to the carrier.