NFA Items are firearms governed by the National Firearms Act. It includes Short Barrel Rifles (SBR), Short Barrel Shotguns (SBS), Machine Guns, and Any Other Weapons (AOW). Yes, you can own these in Massachusetts… kind of.
Unfortunately, since Dec 2017, the AG has determined that MA Dealers may no longer transfer these to mere mortals. That includes LE! MA now applies the same rules that apply to pistols to NFA items, so these now have to be on the EOPS roster to be transferable. Fat chance of that happening. This ruling does NOT prevent you from legally creating your own SBR. But, unfortunately, you are on your own there.