In his Handbook on the New Testament Use of the Old Testament, Greg Beale lists "the most important 'background' commentaries" for seeing how other Jewish sources interpreted a text that is being interpreted in the New Testament, but Logos carries only a couple of these. Can we get the others in the works?
Boring, M. E., K. Berger, and C. Colpe, eds. Hellenistic Commentary to the New Testament. Nashville: Abingdon, 1995.
Braun, H., ed. Qumran und das Neue Testament. 2 vols. Tübingen: Mohr Siebeck, 1966.
Chilton, B., D. Bock, D. M. Gurtner, J. Neusner, L. H. Schiffman, and D. Oden, eds. A Comparative Handbook to the Gospel of Mark: Comparisons with the Pseudepigrapha, the Qumran Scrolls, and Rabbinic Literature. The New Testament Gospels in Their Judaic Context 1. Boston: Brill, 2009.
Instone-Brewer, D. Traditions of the Rabbis from the Era of the New Testament. Vol. 1, Prayer and Agriculture. Grand Rapids: Eerdmans, 2004.
———. Traditions of the Rabbis from the Era of the New Testament. Vol. 2A, Feasts and Sabbaths: Passover and Atonement. Grand Rapids: Eerdmans, 2011.
Keener, C. S. The IVP Bible Background Commentary: New Testament. Downers Grove, IL: InterVarsity, 1993. Unfortunately, this commentary typically does not contain primary source references to either the Jewish or Greco-Roman sources on which so many of the discussions are based. Nevertheless, when there are discussions of background, it should alert the student to try to find the primary sources on which these discussions are based in order to evaluate them and to see if any of them represent Jewish interpretations of the OT.
Lachs, S. T., ed. A Rabbinic Commentary on the New Testament: The Gospels of Matthew, Mark, and Luke. Hoboken, NJ: Ktav, 1987.
Lightfoot, J., ed. A Commentary on the New Testament from the Talmud and Hebraica: Matthew-Corinthians. 1859. Repr., 4 vols. Grand Rapids: Baker, 1979. Lightfoot uses archaic references when citing the Talmuds, so the researcher may need to use some ingenuity to trace these references.
Strack, H., and P. Billerbeck, [Str-B] eds. Kommentar zum Neuen Testament aus Talmud und Midrasch. 5 vols. in 6. Munich: Beck, 1922–56, http://trove.nla.gov.au/work/797911. This can be a good source for finding references, though one needs to keep in mind some of its shortcomings.
Strecker, G., and U. Schnelle, eds. Neuer Wettstein. 3 vols. New York: de Gruyter, 1996.
Wettstein, J., ed. Novum Testamentum Graecum. 1751–52. Repr., 4 vols. Graz: Akademische Druck- & Verlagsanstalt, 1962.