As far as my poor understanding of the matter goes, the chassis number is on the chassis, so the identity of the car is tied to the chassis. If you were to bring in a chassis and stamp your current number onto it, there would then technically be two cars with the same chassis number.
To do it legally, you can bring in the chassis and use it to build a car using a donor body, but you have to register it as an ICV, which means modern engine and possibly other things. The guys that built the mustang fast back for that Koshi guy on morning TV used a brand new shell and that's the way they went about it, hence it's powered by an LS engine.
Again, that's only my understanding and I could be completely wrong.