I've had this conversation with a few people regarding Park Mammoth in Kentucky. After some internal debate on the subject, I decided that enough was done to constitute a redesign, or to call it a new course. The owner agrees. Others, including some on this thread, don't.
There, not a single hole has the exact same tee location, centerline, and green location, yet almost every hole utilizes at least one of the three. Some of these routing changes were minor, others major, but we only went outside the original footprint of the course in one spot. We doubled the green square footage and completely redesigned every element of them save for one green (#9). We added length where we could, added 25 bunkers (there were none on the previous course), and removed the vast majority of the trees on the interior of the property. I don't think there's a person alive who has seen both versions that wouldn't call it a major transformation, but whether it's a "new course" or not is certainly up for debate (if necessary).
I say "if necessary" because, while I have my opinion, at the end of the day it really doesn't matter to me. I'm just proud that we were able to take something that was below-average, dying, and an after-thought in its own small market, and create something that's really worth seeing (IMO). How it's remembered 50 (or 100) years from now is pretty inconsequential to me and my guess is that guys like Donald Ross and his peers probably didn't put a lot of thought into the matter either.