And the fun of thinking about the future shall begin once more! For the most part I'll attempt to be "frank" with my thoughts of what "could" be done.
I'll start with story:
There are a few questions that will need to be answered before this can be put into motion, starting with whether the new story line will take place at "endgame", for players who have finished most of the game's current content (And in this case assume that they are level 40+ players with a few weapons/skills already maxed), or whether this new story content will be able to be accessed by newer/lower level players (Effectively 10-20 level, a bit past just freshly joined but still have plenty of things to do). What this choice gives us, is either to make completely new/fresh story content that will take place after the Black Pearl quest line and the current content (For level 40+), or to make new content that coincides or adds to the continuity of the current content in game (Something that players level 10-20 can pick up and possible do alongside current quests and still have the story make sense). Depending on which of the choices you pick, will lead to my next thoughts on this subject.
New/Fresh "End Game" Content:
I would have this form of content start at a point where the main story has been completed and you have a clean slate to work with. There are many ways you can go about this, but the first thing that I think should be confirmed first, is what is at the end of this new content? Mainly, what reward will be given to the player? Rare/Epic weapons? Access to new island(s)? Perhaps you may even decide to give the player a new kind of Ship altogether? Perhaps they unlock a new form of skill or special feature you have decided to introduce?
(Side Note:If it is a game changing feature however, I would almost have the quest start earlier if it is a feature that will take time to get used to)
If you just want to skip too what I want to add, begin reading here:
What if you made a new island, whose main enemy were the "Cannibals"? Along with this new type of enemy you can now weave a completely new story separate from the current content and still have it coincide with the movies(Assuming you are trying to have your story line connect with the movies, in which if you don't, that is completely fine an has a whole different range of possibilities). Along with the story, this could add an array of items that could change how we play, or add to it. Firstly, you could add different weapons. And no, I don't mean you have to add completely new skills, but let me give a few examples: Blowgun, you could make them usable under the "shooting" skill. Hand-axes, these would be a bit tricky, but perhaps you could have throwing hatchets along with daggers? And my last thought, Spears. These are hard to picture where they would go, but try to hear me out. What if... they were a form of Staff? Voodoo powers with Melee combos? Yes that would take a fair amount of balancing and be hard to do, but I thought I might as well throw it out there. Of course you should be able to add "Cannibal"-inspired swords, voodoo dolls, and a few daggers as well, but the first three would need more than just a re-skin of a different model. Moving on from weapons, we also have Aesthetic items as well. You could add a fair amount of new tattoos or clothing pertaining to the Cannibals. Maybe the players Do want finger/toe necklaces? You never know.
Of course if you don't want to use specifically the Cannibals, what about adding an island of Aztecs? You could keep most of the changes I mentioned, just under a different name. And you don't need to have the Aztecs specifically as "enemies" either. Just a bit of a side thought.
Moving on to early/mid-game content (Level 10-mid 20's):
This I believe would be harder to make story-wise, assuming you want it to be compatible with the current "World". Unless you already happen to be planning a complete rework of the world and story in game, there is only so much you can do. However, you could do a simple quest chain consisting of islands that already exist, perhaps even using NPC's that already exist for plot points and such.Otherwise you "could" add another weapon type, but going more than the six we have will add an extreme amount of unneeded hassle, or so I think anyway.
I honestly don't have any particularly good ideas for this range, other than that if you have new integral or important features to be used in game coming out, the sooner they are given to the player base so that they can become accustomed to using said feature, the better.
If we are just looking at smaller features to be added, these are a few that have already been said, I just want to reiterate them for the sake of their usefulness:
Having a player bank/storage facility, even if it is clothing specific.
Making a guild hub. I can't think of a perfect way this could be done, could go from having a guild "Island", or something a bit more feasible, like a guild Tavern or Trading house of some sort.
Going into the actual depths of a ship is also quite an interesting idea.
That is kinda it for my thoughts on the subject, even if the ideas themselves aren't useful on their own, perhaps it will spurn the creative thinking of other Pirates looking toward the horizons of this world, Aye?