It is possible to build just about anything given the time and resources. If you want something like a raspberry pi, you could start with that products schematic as a starting point and begin to make the modification that you desire. With a working schematic you can design a PCB and have it manufactured. Then comes assembly. Given these high level steps, all you need are the knowledge and skills (possibly some equipment) and you can do it.
Figure out where you skills/knowledge is weak and these are the things that you can learn about.
Just a FYI, it will cost you much more than the cost of a raspberry pi to build one.
