I wouldn't do that. A replacement chassis is perfectly acceptable. Stamping numbers into frames is a crime in many juristictions.
A few years ago, the people's republic of Connecticut state police wandered through a car show and started impounding vehicles where it was obvious that the owners had removed the vin plates (rather than mask and paint around them) and re-riveted them back after refinishing regardless of whether the numbers matched other stamped locations. Lots of legal wrangling for the owners to get them back before they were sent to the crusher.
A buddy of mine (Pat Dennis, who I'm sure some of you know...) sold his S2 with a Brian Hart twin cam/5-speed conversion and the subsequent owner proceeded to stuff the car into a barrier, essentially destroying it. Somehow, the windshield and bonnet plates ended up in Canada on a road/race car, registered in Ontario...Jerry and I discovered it while updating the registry...and I got the original info (xerox of the title, registration, and photos of the destroyed car) from Pat to correct the registry entry, much to the current (at that time) owner's dismay. Don't know what the follow on was, but I can tell you he was NOT pleased.
I made it a practice, from all of the cars I broke up, to destroy the plates and turn in the titles. Got more than a few folks who asked if I wanted to sell them back in the yahoogroups days, believe or not. Never did.