I may do a series of posts on the scholarship of Erhard Blum. For the time being, I'll draw from Ernest Nicholson's The Pentateuch in the Twentieth Century, but I may eventually draw from other sources as well.
On page 98, Nicholson sums up Blum's overall argument: Blum "argues that a Deuteronomistic redactor of the early post-exilic years reworked a pre-exilic 'history of the time of Moses', joining it with a (pre-Priestly) narrative of the patriarchs. This Deuteronomistic work (KD) subsequently underwent a Priestly redaction (KP) which gave us the Pentateuch substantially as we have it. For Blum, therefore, as for Rendtorff, the notion of continuous and originally independent sources such as J, E, and P must be abandoned."
When reading Blum or reading about his work, I get intimidated when I see "KD" and "KP", for I'm not accustomed to those designations. But I need to remember that I'm just dealing here with the Deuteronomist and P. Whereas many scholars date the Deuteronomist to the time of Josiah, or to the exile, or to both, however, Blum dates the Deuteronomist to the early post-exilic period. For Blum, the Deuteronomist joined stories about Moses with the pre-priestly narrative of the patriarchs (which I take to mean that there are also priestly, or perhaps post-priestly, stories about the patriarchs). I vaguely recall from Farewell to the Yahwist that Blum modified his position in areas, but his position on the Documentary Hypothesis is the same: he does not think that there is a J source or an E source that runs through the patriarchal and the Moses stories, for his very point is that the patriarchal and the Moses stories were separate and independent---and were brought together at a stage of redaction.
On pages 116-118, Nicholson presents an example of this. In Genesis 25-33, there is an "originally independent narrative about Jacob" that includes "the cult foundation legend of Bethel in Genesis 28:10-19 (without the promises in vv. 13-15) and the Jacob-Esau-Laban narratives in chapters 25:19ff.; 27-33" (page 116). The Jacob-Esau-Laban narrative was combined with Genesis 28:10ff. (the foundation of Bethel) "by means of Jacob's vows in 28:20-2 and the theme of reconciliation between Jacob and Esau" (page 116). According to Blum, this occurred under Jeroboam I, for Jeroboam exalted the site of Bethel and, as an Ephraimite, elevated Joseph. In Genesis 33, the story of Jacob's reconciliation with Esau, Joseph is presented as special to Jacob.
In the eighth century, the Joseph story (Genesis 37-50) was composed, and it was later combined with the Jacob story. After the fall in Northern Israel in 721 B.C.E., "this northern Israelite complex was given a Judaean orientation by the incorporation of chapters 38 (the story of Tamar) and 49 (the blessing of Jacob) both of which give prominence to Judah among the sons of Jacob" (page 117).
Then, according to Blum, the Jacob-Joseph complex was combined with the originally independent Abraham-Lot complex, which is Genesis 13, 18-19 and focuses on the people descended from Abraham and Lot. For Blum, we do not have the beginning of this story, and Genesis 12:1-9 (the land promise and Abraham's migration) does not count because it presupposes the larger patriarchal narrative, and the Abraham-Lot stories appear to be out of place with that. But the Abraham-Lot complex was combined with the Jacob-Joseph complex through the promises in Genesis 13:14-17 and 28:13-15. According to Blum, this occurred between the fall of Northern Israel and the destruction of Judah in 586 B.C.E., and this was also when the promise speeches emerged. Other independent stories were added during the exile---Genesis 12:10-20 (Abraham in Egypt); 16 (Hagar); 21:8-21 (expulsion of Hagar and Ishmael); 22 (the akedah); and 26 (Isaac and Abimelech). Meanwhile, "the theme of the promises to the patriarchs was extended to other contexts in Genesis 12-50."
The Deuteronomist then connected the patriarchal narrative with "the other major tradition complexes in the Pentateuch" (i.e., the Exodus, the Conquest) by means of Genesis 15 (which mentions the Exodus and Conquest) and 24 (the story of Rebecca). Then P added tables of generations and chronological notices.
UPDATE: I’ve learned that Blum actually distinguishes KD from the Deuteronomist, for he believes that KD was later—an heir to the tradition of the Deuteronomistic School.