The two ways that stuck out to me came from Benjamin and Burke. Benjamin, in The Work of Art in the Age of Mechanical Reproduction, frames interpretations in terms of how they are framed more in a literal sense, as mechanical reproductions of works of art attempt to be accurate and transcend that issue of time and space. Burke takes a different perspective as he looks at how the original nuts and bolts (terms) can be used in different ways for vastly different outcomes of interpretation. What I got from these theorists is that is comes down to a question of intention. Burke and Benjamin both deal renovations of things that already exist, but Benjamin is interested in maintaining integrity while Burke is more interested in new ways of seeing old works.
This can best be understood in comparing how they deal with the reproduction of photography. Benjamin is extremely concerned with maintaining at least a semblance of the integrity of the original as he writes, "technical reproduction can put the copy of the original into situations which would be out of reach for the original itself . . . the situations in which the product of mechanical reproduction can be brought may not touch the actual work of art, yet the quality of its presence is always depreciated"(1235). In contrast, Burke writes, "When I speak of 'terministic screens,' I have particularly in mind some photographs I once saw. They were different photographs of the same objects, the difference being that they were made with different color filters"(45). Benjamin is conscious of the depreciation and sees something of a misfortune in it, while Burke much more embraces the difference and mutability of "something so 'factual' as a photograph," as he puts it.
So does the integrity of an original suffer in reinterpretations or is glorified in the appreciation of other artists to portray it in different ways? I'm still not sure, but I think there is value in maintaining an awareness of the original with its historical context and original interpretation, otherwise we would end up in a world of creative mutability lacking in the hierarchy that often inspires artists to create in the first place.