My predictions:
>It's not just an alternate story; it's an alternate dimension. At some point, you will be able to visit the original Sun & Moon dimension.
>In this dimension, Akala Island's volcano erupted ages ago, breaking apart the island into several small islands. Pokemon that could be found easily on that island will now be much harder to find, especially ones that lived near the volcano itself (Cubone, Salandit, etc.).
>Because of the new island formations, there will be new trials, with new Totem Pokemon.
>Gyms will return, but will go hand in hand with trials. You will only be allowed to challenge the gym leader if you have the Z-Crystal from their trial. The Grand Trial against the Kahuna will still be required before moving on.
>The player character is an Alolan native instead of the new kid that just moved in.