I’m aware that according to Lore there are only 6 (7) Sirens. That limit was cool in earlier BL titles, but now its starting to get a little crowded on the Siren scene. We already know about 5 siren powers.
We also know the Eridians used the Sirens to help construct and control the vaults. The Eridians also sacrificed their entire race to power the Great Vault. What if the Eridians also sacrificed Sirens to construct the Vaults?
What if each of the lesser Vault Monsters was a construct that used a Siren as the core of the monster? Or if the control circuit of major vault components had a Siren sealed into them to act as a sort of management system? That would explain why other Sirens can instinctively interact with the vaults, because a similar power is currently managing the device, and it wants to connect with other sirens.
BL4 could be about finding these sealed sirens and freeing them. BL5 could be dealing with consequences of breaking the control devices on the Great Vault. BL6 could be largely focused on a war between large groups of new Sirens trying to control Pandora as the largest single source of Eridium in the universe.
BL5 could be really interesting because one of the goals would be to find a way to replace the sirens released from the Great Vault. While Tannis is the foremost scholar on the Eridians, she may not be the best candidate for coming up with a solution. Atlas and then Hyperion are the companies that operated on Pandora the longest. Maliwan has experience with Eridian technology as well. If the developers want to try and appeal to BL2 fans they could bring back Holo-Jack as an expert to help produce control devices. Sure its a deal with the devil situation, and of course there will be a betrayal or three but it keeps things interesting.
Or you make Holo-Jack the guy hiring vault hunters and this time he actually gets to be the hero, with Holo-Jack’s little empire getting wrecked by a Siren Uprising in BL6.