Could at any time the Bible be reorganized or re-canonized? What would it take to make that happen? Who would be the authoritative body to do that?
The Bible has already been reorganized and re-canonized more than once. The Roman Catholic Bible, for example, has a different organization than the Protestant and the Jewish ones. Each of these three Bibles contain different books organized in a different order in order to satisfy the theological assumptions of their ecclesial bodies. So, in reality, we don’t have one Bible, but three.
Nothing more than this should be expected. It is actually a good thing, because it adds diversity to how the Word of God is conceived. For some people the books of the so called Apocrypha are as much the Word of God as the book of Genesis. For others, Jews for instance, they are not. To suppose that a single authoritative body could reorganize or re-canonize the Bible is to throw us back into the Middle Ages, and no thinking individual today would want that.
Would it be possible for each of these individual ecclesial traditions to carry out the kind of task asked by this question? Very unlikely, but even if it would be possible, it would be an unsurmountable job with negative consequences. In my opinion, it is better to leave the “Bibles” as they are and spend our time and energy in celebrating difference instead of forcing sameness.