Board Thread:Fanon Canon/@comment-2089817-20180513110249/@comment-1493741-20180520061148

Well, they essentially defected and engaged in open rebellion so the obvious thing is that they're dissatisfied with the current status quo, I believe the early talks on the group had been around it finding out about the original sin especially given how closely connected to the innerworkings of the Soul Society they are. Since they didn't stake their claim from their headquarters in Soul Society, but chose to flee, then they're first goal is pretty straightforward.

Independence. Since we've timeskipped several years, the Kidou Corps turned Coven will have already established a base of operations, a new chain of command centered on its rebellious leadership and now need to seek means to maintain that independence. They are the underdog, vastly outnumbered (and outpowered?) by the Gotei 13 and Onmitsukidou. If Arc 1 is their attempt to build up their numbers by kidnapping and pressing all sorts into service, then Arc 2 is them trying to confirm their suspicions and build up information that prevents the Soul Society from dropping a Kidou Cannon on their asses.

So there's some short term goals. What they want in the long term, I have no idea.