Sure. You'll need to buy all the parts, get all the non-disclosure agreements from the chip makers to get the documents to learn what you're supposed to do, come up with a schematic, layout and route it, and then have a professional production line manufacture it.
Then, to find out whether the thing is even remotely working, you'll need to license and port a BIOS core to your design. Next you'll need advanced diagnostics tools, both hardware and software, to debug your prototype and assert its workingness and standards compliance in all aspects, from core busses down to every single peripheral I/O. Then enter round two of schematics/layout/prototype and see if that one got better. After a couple of iterations, when you think it's good enough, get serious about teaching your crude BIOS everything it needs to do to let a modern operating system even think of running, PnP, ACPI, blahblahblah. Done that? Good. Start writing/porting drivers for all the peripheral chips you used next.
It's not a spare time project. If you seriously want to do these things, start a career in that direction. In about five to ten years you'll have learnt enough to get assigned your first mainboard project.
Note: I do not want to sound discouraging at all - it's a rewarding path, and a really fine job with a perspective. Just know the dimension of the task.
I second what others have said: Start small. If you want to toy around in your spare time, try figuring out something much simpler like a PCI I/O card, made from parts and using busses and ports whose specifications are public.