I've always been fond of the idea of being able to travel across space and time to see crucial parts of history or the past. Aside from giving the player something to do, it does help in explaining why things are set up as they are. Games like Chrono Cross in particular managed to use this to explain and expose things that would have been difficult to convey to the player.
Now, people who played FFXI will remember that the maws and Atomos played a role in our being able to move through time and between worlds. As such, I though that it would be neat to use this not for an expansion, but as a way to present content related to Eorzea's past to the player by letting them be part of history.
Concept
In the five years since the fall of Meteor, the Circle of Knowing has endured inner turmoil between its members over what their role should be in this new world. Without the leadership of Louisoux to keep the circle together, several members have broken off to form the Pearled Enclave.
Unlike the circle, who focuses on studying Eorzea's mysteries and understanding the world and its magic (note: I made that part up), the enclave aims to forcibly bring change to the world. Using information obtained by studying the maws of Atomos before Meteorfall, the enclave is attempting to:
A) tamper with key moments in Eorzea's history under the delusion that it'll be for the better
or
B) tamper/sow chaos in the new worlds accessible via the maws
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As I see it, players would be able to use the maws to go into the past if we go with Option A. Say, the enclave is trying to meddle with the Battle of Silvertear Lake by trying to change things so that the wyrms win instead of the double KO between the wyrms and the Garleans. The players would enter an instance built and scripted around the battle itself, helping keep history intact. Another example would be the enclave maybe trying to prevent then captain Merlwyb Bloefhiswyn from winning the...err....that race thing with ships, thus preventing her from becoming admiral of Limsa Lominsa.
Conversely, Option B would be more for shout-outs to other Final Fantasy games through the use of the maws. The example that sparked this idea was the enclave ending up in Kefka's Tower just as it is collapsing after the final battle, and the players would have to fight behind the scenes to ensure the Final Fantasy VI cast makes it to the Falcon and fly out in time.
It needs a lot of work and fleshing out, but that'd be the basic idea.
tl;dr - Use Atomos as FFXIV's version of the Caverns of Time.