Building multiprocessor motherboard
Inter-processor communication is possible and as you indicate some kind of bus arbiter would be needed for shared memory. I don't want to steal your joy, but what you are describing is a huge project. Unless your school lab is really advanced it is also likely that the PCB technology needed for this build (multi-layer, narrow isolation and maybe microvias) is missing. 

If you want to experiment with parallel computing maybe a dual-core microcontroller (processors + peripherals in one package) would be a good start. You can find some LQFP packages that are easy to solder. An even better way could be to study an existing design such as the Pandaboard (http://pandaboard.org/).