Modern detailed study of Midrash must take note of the concept of exegetical motifs. A motif is a thematic unit that may combine, double or reconstitute in different Midrashic passages to produce a variety of passages that resemble each other but also vary in significant ways. These exegetical units initially explain a textual or theological peculiarity; however, in time, they affect and serve as models for both Midrashic and pshat based interpretation. "Motifs, and individual elements belonging to them, often become combined or harmonized with other motifs…behind it usually stands an attempt by the exegete to reconcile two traditions, both of which he considered authoritative.. ".
When combined with the historical method, there emerges a powerful tool to understand unfolding and relationship of various Midrashic passages. Historical methods have unfortunately often been used of pull down and destroy and they have not enjoyed full trust or acceptance among traditional scholars. An exception has perhaps been in the filed of Mishnaic studies, where the existence of the proto- mishna, the so-called mishna rishona, is universally accepted and attempts to reconstruct this original mishna are tolerated by all segments of Torah community.
Close study of halachic midrash leads me to the conclusion that Mekhilta and other midrashim were also built around an ancient core of pshat interpretation. This core may have been taught and committed to memory in schools and academies together with the written Torah text. This core consisted of short explanatory statements, used expression "shene'emar" and was passed on orally. It dates to very early within the Second Temple period, perhaps to the time of Anshei Kneses Hagdola, perhaps even to the First Temple period . These statements were subsequently expanded, often with words "vken hu omer" and are in a different style than the core. It is in this later strata that we find disagreements among Tannaim. If so, we should expect the different ancient exegetical motifs to also be found in other early midrashic collections, such as Pirkei D'Rabbi Eliezer, and they may turn up in expanded version, alone or side by side, or in a reconciled version in later Midrashic collections or in the Talmud.
Let us look at an example.
Between me and the Children of Israel a sign it is forever, for in seven days Hashem made heaven and earth and on the seventh day he ceased and rested (Shemos 31,17).
There is both an exegetical and theological difficulty in this verse. We must explain the deeply private and personal connotation of "between me and Children of Israel". We also need to explain in what way are Gentiles excluded from this private "sign". Are they unable to take on some Sabbath observances? If, as we know historically, they have done so to some extent, in what way is it then a sign solely between G-d and the Jews. The first Midrashic passage that we cite understands this "sign" as signifying an act of covenant, and it was private because it was in secret; the second as an actual handing over to the Jews of something that other nations cannot access, even if they know about the Shabbos and attempt also to observe it.
Between me and Children of Israel - and not the nations of the world (Mekhilta).
This very short phrase clearly belongs to the core. It appears to have been subsequently interpreted in two different ways. Some midrashim see it as a halachic or aggadic proscription of a non-Jew keeping Shabbos. Others understand it as a statement that the act of giving the commandment of Shabbos was originally performed in secret, in order not to allow the nations to copy it in their own rituals or religions .
The Holy One Blessed Be He said to Israel : I gave Shabbos between me and them…blessing, holiness and rest for Me and them.. (Pirkei D'Rabbi Eliezer, 18) 
This passage proposes that Hashem gave blessing, holiness and rest only to the Jews who keep Shabbos. Were a non-Jew attempt to observe Sabbath, he or she would not experience these things. In this fashion it is a sign between God and Jews exclusively .
The Talmud in Betsah 16a attempts to reconcile these two disparate traditions. I do not mean to imply that its reconciliation was not present at inception; quite possibly the later source simply reports how the two traditions were reconciled already at the time that the early midrashim were composed (and we have seen examples of this in phenomena in previous installments of Midrash and Method).
R. Yochanan said in the name of R, Shimon Bar Yochai: All commandments that the Holy One Blessed Be He gave to Israel, He gave to them in public except for Shabbos which he gave to them in secret, as it says, "Between Me and Children of Israel".
If so, Gentiles would not be punished for (for not accepting it, Rashi)!
(No,) He informed them about Shabbos but He did not inform them about its reward.
Another answer: He also informed them about its reward but He did not inform them of the extra soul (Neshama Yeseira).
This Talmudic passage combines the two traditions. It first cites the tradition that Shabbos was given in secret, to Jews but not to nations of the world (Motif #1). In its second answer it brings in the motif #2 - that the essence of the 'sign' was that Gentiles cannot participate in "blessing, holiness and rest".
The concept of exegetical motif must be used carefully and cautiously and with full attention paid to Sinaitic origins of the Oral Law. Those caveats aside, it can be a powerful toll that enables to systemize various related Midrashic passages around several basic themes that often can be shown to have their origin in early Tannaitic midrash.
1 J. Kugel, In Potiphars's house: The interpretative life of Biblical tests, Harvard University Press, 1990, p. 256.
2 There are many verses in Chronicles, for example, that are repetitions of verses from Kings or Samuel but with a word or few words added. These may represent traditional oral explanations of these books that were ultimately committed to writings under the influence of Ruach Hakodesh (for status of Divrei Hayomim vis-à-vis Ruach Hakodesh, see Pnei Moshe and Amudei Hayerushalmi to the very end of 1st chapter of Yerushalmi Bava Basra).
3 Torah Shelema Tisa, 96 quotes a number of examples of such midrashim.
4 As the Radal points out in his introduction to PRD"E, it is the second work of Oral Law to have been committed to writing (the first one was Megillas Ta'anis), significantly before the time of the Mishna.