Probably not, at least in the United States. The new texts would receive a new copyright, but the old ones would still enter the public domain at the same time as they would have before.
Imagine I created an annotated critical text of Oliver Twist. My new annotated text would be copyrighted from the date of publication, but Oliver Twist would still be in the public domain.
But what if you could get the original text cancelled? No right-thinking publisher would print it, no God-fearing bookseller would stock it, no teacher who valued their career would add the unsanitized version to their school library, and they would buy your annotated version instead.
I suppose someone could create a second censored version, but if the changes they made were too close to the current publisher's, they might lose a copyright case on that. So all the publisher has to do is keep up with the mores of the time on what must and must not be airbrushed out.
> But what if you could get the original text cancelled? No right-thinking publisher would print it, no God-fearing bookseller would stock it
Modern book "cancelling" is not (yet?) so effective as that. Huckleberry Finn is a popular target for cancelling, yet is still widely available. Being in the public domain gives the book relative safety; even if one publisher gets cold feet, another will jump in to fill the demand. The real threat is to books which aren't in the public domain and won't be for a long time.