Old Testament scholar Brooks Schramm describes the history of Third Isaiah explanations.
Brooks Schramm, "Introduction: Third Isaiah?" in The Opponents of Third Isaiah: Reconstructing the Cultic History of the Restoration (Sheffield: Sheffield Academic Press, 1995), 15
At this point in the history of the discussion of Third Isaiah there were three major alternatives. Duhm saw Isaiah 56-66 as a literary unity dating to the mid-fifth century; with Duhm, Eliiger also viewed the chapters as a unity, but assigned them to the early restoration period, c. 520 BCE; Volz rejected the unity of the chapters and spread the oracles over a period of some five centuries. The only other alternative was to deny the basic thesis of Duhm and argue that there is no Third Isaiah. Obviously, if one accepts either Duhm or Volz, then Second Isaiah could not have composed chs. 56-66. On the other hand, Elliger's claim that the chapters date to the early restoration period makes possible the argument that Second Isaiah could have written them.
In spite of all the controversy over 'Einheit', the most difficult problem in the study of Third Isaiah is that of when to date the various oracles. The material is notorious for its lack of any sort of concrete historical reference. Neither foreign nor native Judean rulers are mentioned. Coupled with our general lack of knowledge of the historical events that took place in the late sixth and early fifth centuries in Judah, the problem is compounded.