There's Rabbi Mordechai Breuer's "שיטת הבחינות" - "Theory of Aspects". He first presented it in this essay, published in 1960.
Rabbi Shalom Carmy in his essay "Concepts of Scripture in Mordechai Breuer", Jewish Concepts of Scripture, ch. 15, summarized the theory:
"On the one hand, Breuer maintains that all the literary phenomena adduced by the critics to show that the Pentateuch is the product of multiple authors are compatible with divine authorship. On the other hand, he insists that unitary authorship by a human being is impossible. In each instance when the critics posit multiple authors, Breuer too discerns different voices. One task of the religious student is to grasp each of these voices in isolation, unearthing the theology, narrative vision, or legal positions implicit in each one. Finally, one also investigates the ways in which the Torah as a whole integrates and mediates these voices. No human author, in his opinion, could have orchestrated this multiplicity of voices. Thus, either the critics are right, in which case we have a jumble of
conflicting writers spliced together, or there is a divine Author expressing a complex message by employing different voices. This, in a nutshell, is Breuer’s thesis." (pg. 268)
To summarize even further, Rabbi Breuer held that Hashem purposefully wrote the Torah in a contradictory manner because it reflected the multiple aspects of Hashem - Din (judgement), Chesed (grace), etc. It is this exact contradictory manner that shows the Godliness of the Torah.1
Rabbi Breuer first began developing the theory because he had come to accept that much of the central points of the Documentary Hypothesis made sense. As he wrote in his first essay (my translation):
"We will not complain about Spinoza who wished to prove the later dating of the Torah - from the words of the Torah itself. Indeed, the twelve sections that are brought in the Ibn Ezra's commentary, and are copied in Spinoza's essay, prove beyond a shadow of a doubt, that this Torah - within the frame of possibilities of the laws of literature and history - was written in Eretz Yisrael many generations after the conquest. Indeed: No man could have listed the kings of Edom alongside the kings of Yisrael, or that the Canaanites were "then" in the land - in the era before Yehoshua..." (6th section, 1st paragraph)
In light of the DH, and after discussing the classic harmonistic explanations for contradictions in the Torah, he writes (my translation):
"But perhaps it is the opposite? Perhaps we should not decide the form and content of the Torah, but rather we will learn from the Torah [itself] what form and content it has decided for us? Perhaps we should cancel our will before His will and believe in the unity of the Torah - out of the multiplicity of its sheets? Has not the time come that we free ourselves from the weight of all mortal views, and to learn the Torah of Hashem - without any prior prejudices? Is the Torah really only straight and bringing of happiness - out of the outdated, harmonistic exegesis? Truly, can't the Torah be beautiful and graceful - even when it remains as it is?" (11th section, 3rd paragraph)
Rabbi Breuer concluded that the key to the DH is Torat Ha'Sod. As stated above, each contradiction may be solved by saying that it reflects a different aspect in Hashem's "essence".
Stating that different names of Hashem represent different aspects of Him is, of course, nothing new, but it was Rabbi Breuer's idea to turn it into a key (not a weapon!!) to the DH. With that said, Rabbi Carmy in his own essay thought that Rabbi Breuer was inspired to reach this conclusion by a number of figures. The first two were his great-grandfather the Rashar Hirsch and his uncle, Rabbi Dr. Yitzchak Breuer. They were the proponent and "the most creative exponent" of neo-Orthodoxy, respectively. Dr. Breuer's views were heavily inspired by Kant and Kantian thought.
The next source of inspiration was Rabbi Breuer's friend, Rabbi Yehuda Amital:
"Breuer claimed that the need to assimilate biblical
criticism prior to combating it was first suggested to him by his colleague
R. Yehuda Amital, whose own worldview is rooted in the mystical teaching of R. Abraham Isaac Kook, the Chief Rabbi of Palestine in the 1920s and ’30s, whose mystical thought has been enormously influential on modern Orthodoxy. The early essays explicitly cite R. Kook, especially his view that heresy is overcome not through immediate rejection but via a dialectical confrontation in which the “palace of Torah” is rebuilt so as to take over what is valid in the heretical ideas..." (pg. 270)
Fourth, Rabbi Breuer was likely inspired by the Brisker method of gemara study, the "צווי דינים" (two laws) method, which solves discrepancies within certain laws in the gemara by explaining that each POV is referring to a different aspect of the same situation.
Finally, he may have been inspired by the fact that there have been several commentators over history who have used both p'shat and derash in their commentaries, without seeing any apparent contradiction in this.
1 Similarly, no two prophets prophesize in the same style - because saying that there is only one style of Hashem limits Him.