No. But not surrendering the data plate and airworthiness certificate, many people have "repaired" planes by replacing parts one by one (wink wink nudge nudge). Legal? Perhaps, perhaps not. Kinda like the guy with Abraham Lincoln's axe... the head was replaced once or twice, and the handle has been replaced a few times, but it's still Abe's axe...
The Taylorcraft I used to own at one point (before I owned it) had the fuselage replaced with a new fuselage, later the wings were replaced with a set of "good used wings". I don't think the tailfeathers were original, either. As near as I could tell, the only certain original parts were the engine (maybe) and the landing gear. But it was still a 1941 T-Craft.