Old Testament Scholar R. E. Clements argues that there is a unity of theme (but not authorship) across Isaiah.
R. E. Clements, "Beyond Tradition-History: Deutero-Isaianic Development of First Isaiah's Themes," Journal for the Study of the Old Testament 10, no. 31 (1985): 110–111
If we are also to press the questions concerning the origin of the material in Isa. 40-55, which has come conventionally to be ascribed to ’Second Isaiah’, then it would seem that the case for recognizing the contribution made by cultic personnel, the so-called cult-prophets, from Jerusalem is very strong. This has been argued for by J. Vincent, and it appears to be an increasingly probable deduction to make from so much of the recent research into the origin of these enigmatic chapters. Whether this must imply an actual origin in Jerusalem appears to be less certain, and the possibility of a Babylonian setting, as so widely advocated, may be correct for at least some of the material.
A further consequence also appears to be worthy of further consideration and investigation. If the sixteen chapters which have usually been ascribed to ’Second Isaiah’ are really the work of one man, then they stand unique within the otherwise intricate web of prophecy and prophetic interpretation which constitute the remainder of the book. Nowhere else do we have such a solid and undisturbed block of material left intact. This is not in itself a reason why it should not be the case here. Nevertheless there do appear to be indications that in respect of some material, as in the admonitory rejections of idolatry, later hands have been at work. Overall the formation of the Old Testament books of prophecy has been a remarkably complex sequence of literary and theological developments of ancient written texts. The assumption, which was really never more than an assumption until the end of the eighteenth century, that the unity of these books can be explained as a unity of authorship is clearly mistaken. Yet they do possess a certain kind of unity which belongs to the nature of prophecy itself and the various ways in which it was applied to historical events, which alone could provide its fulfilment, and so, in a real sense, which alone could establish its true meaning.
We might be disposed to describe the processes of unravelling the intertwined threads by which such a book as Isaiah has taken shape as 'Redaction Criticism’. Yet, if this is to be so, it behoves us to keep in mind that this is concerned with very different kinds of redactional operations from those which pertained to narrative texts, where the combination of smaller units and themes has been undertaken from quite different perspectives from those which belong to prophecy.