I also like the idea, if only for modding potential, but unfortunately, there is currently no way to make such a mod since items don't give stats (only armour does).
You could make a mod where aliens sometimes drop artifacts that can be used in the manufacture of special armours though. But it still would just be a stat boost.
There is functionality to redesign the inventory and add a new 1x1 slot, but nothing to restrict what goes there either. Could be an alien artifact, a grenade, could be a weirdly shaped piece of alien rock. (Hum.. better be careful where you put that slot too...). I believe that Yankes' OpenXComExtended allows for restrictions in what craft weapons can be equipped and might have inventory restrictions as well.