Early Alternative Theories

The two most notable alternative theories proposed early on are called the Fragmentary and Supplementary Hypotheses. The former was advocated by Alexander Geddes and J. S. Vater (along with W. M. L. de Wette) at the turn of the nineteenth century. Its chief characteristic, in distinction from the earlier source theory, was that the Pentateuch evidenced that it was made up of smaller fragments "independent of one another and without any continuity, but simply placed together at the hand of a redactor." Although this theory was built upon its analysis of legal material within the Pentateuch, the names in Genesis, as in all stages, including arguments given today, gave rise to the basic understanding that differing sources are used. To the fragmentary hypothesis, however, these became the two groups that collected the fragments. The fragments themselves did not constitute a complete and consistent history by J or P (understood at this time as E).
The supplementary hypothesis that followed, and only replaced for a short time, the fragmentary hypothesis was advocated by Ewald, ironically, who would also be the one to reject the position. In this theory, Ewald proposed that the E source was the foundational story of the Pentateuch. The compiler supplemented material into his account from other sources (e.g. the Book of the Covenant). Later, J (a coherent source supplemented by other sources as well) was added to E in a submissive role to the latter's primacy.
Ewald then argued that the Pentateuch was made up of two continuous and coherent strands (E1 and E2) that were unified and later supplemented by J as an equally coherent strand. As Eissfeldt notes, "We thus have a kind of combination of the older documentary hypothesis and the supplementary hypothesis presented as a solution of the Pentateuchal problem by Ewald, Knobel, Schrader, and others.
These two theories laid the groundwork for the New Documentary Hypothesis.