The term the "Rewritten Bible" has been hotly debated during the last quarter of a century. I use it here in the meaning I gave it when I first launched the concept in Scripture and Tradition in Judaism in 1961: 

In order to anticipate questions, and solve problems in advance, the midrashist (interpreter) inserts haggadic (descriptive or doctrinal) developments into the biblical narrative . . .

The essential feature of the Rewritten Bible is that instead of reproducing separately the biblical text followed by exegetical comments, as does the pesher, the Rewritten Bible incorporates the interpretative remarks into the scriptural text itself. The commentator literally "rewrites" the Bible. This kind of composition may be found throughout the whole of Jewish literature from the Bible itself (Deuteronomy reuses the earlier books of the Pentateuch and Chronicles re-edits Samuel and Kings) to the works Philo, Josephus and the rabbis. However, in recent years transatlantic scholars have tended to restrict research on this topic to the Dead Sea Scrolls. A number of them also object to my phrase "Rewritten Bible" and prefer "Rewritten Scripture". They argue that in the Qumran age the notion of "Bible" was still in a fluid state. But this literary category extends beyond Qumran. Furthermore, is there any difference in meaning between Bible and scripture? Finally, according to Josephus, in his time in the first century CE, Jews recognised as authoritative 22 books precisely. This signifies that there existed a canon, a definite list of works consisting of the five books of the Law (Genesis to Deuteronomy), the 13 books of the prophet-historians (Joshua, Judges-Ruth, Samuel, Kings, Chronicles, Ezra-Nehemiah, Esther, Job, Isaiah, Jeremiah-Lamentations, Ezekiel, Minor Prophets, Daniel) and the four books of Hymns and Wisdom (Psalms, Song of Songs, Proverbs, Ecclesiastes). They made up the Bible, so the phrase "Rewritten Bible" is fully justified.

Before the Dead Sea Scrolls, the principal representatives of the Rewritten Bible were the Book of Jubilees (mid-second century BCE), which retells with inserted comments the story of Genesis and the beginning of Exodus; Josephus's Jewish Antiquities (end of first century CE), covering the whole biblical history; and Pseudo-Philo's Book of Biblical Antiquities (first century CE), concerned with the Bible account from the creation to David. To these are to be added in the world of the rabbis the Palestinian Pentateuch Targums (Pseudo-Jonathan, Fragmentary Targum and Targum Codex Neofiti), all dating from the second to the fourth century CE, but containing much old material. Read out during the synagogue services, the Palestinian Targums performed the same role for the somewhat literate Jews as the visual narration of the biblical story in the frescoes and statues of the medieval churches did for the largely illiterate Christians.