What we call "Judaism" is associated with a Biblical text which descends from the pre-Revolt era. This text supplied all translations of the Middle Ages except for the Greeks', and a few Greek-based translations like the Sahidic and some Syriac. Tradition claims the Masoretes, for this. It was the primary source for the Qaraiya sect of the Jews.
Mainline Jews, famously, use besides their Bible (which is MT) another text: "The Talmud" - specifically, that of Babylonia. This is a difficult text to pin down. It might not have been intended as a final compilation, although it has become one.
The Talmud is aware of the MT but perhaps only as the default Bible. A Karaite would refuse Ben Sira out of hand; the Talmud cites it, and arguably treats it with more respect than (say) Clement was treating "The Gospel Of Thomas". The Talmud is aware of variants in the accepted canon as well, usually ascribed to those pesty Septuagints (in east-Aramaic?) but TheTorah.com cannot rule out old Tanakh scrolls from the Seleucid era. Variants lingered in the Rabbinic tradition even after the Talmud.
It may be that the MT attracted errors which later copyists had to ratchet back - which could end up canonising some errors, rather than fixing them. Similar has happened to the Peshitta which is why Syriac scholars are looking into the earliest Arabic translations.
The Peshitta is, mind, a Christian translation - or has become one. Naturally Jews desired their own Arabic translations. Saadya Gaon created a quick-n'-dirty translation using some Jewish Aramaic lore, which strikes me as creating a Jewish Arabic Peshitta himself. Naturally the Karaites hated it, so redid their own Bible from Ebrea Sola - if I may.