Since you've been asking for this one, here it is: my plot idea for a singleplayer campaign. Now, I need to warn you, this does not take place in Rapture anymore. That city got used to death, and so I wanted to advance the storyline while staying a close as possible to the canon. This probably won't go down well with some of you, but I urge you to at least skim this page before making up your entire opinion. So, here goes:
Works as a "training level". You take control of a Splicer by the name of James, or "Jim" for short, and the date is September 12 1958, in the middle of the Civil War. James is a lieutenant in Ryan's personal army, along with his partner and love interest Laura, and are spearheading the attack against Fontaine Futuristics. He is ordered by his superior, by the name of Cassius Blaine, to lead the charge against the facility and kill Frank Fontaine. After a protracted battle, Laura deals the killing blow to the latter. Immediately afterwards Cassius, under the orders of Ryan, declares the two obsolete and marks Jim and Laura for death. After fighting through waves of their previous allies, Laura leads Jim to a bathysphere to escape to another building. However, as Jim enters the bathysphere, Laura declares her allegiance to Atlas, and executes him by a single pistol shot to the head. She then closes the bathysphere and sends it adrift.
Backstory I: Exodus
This part is discovered through the collection of Audio Diaries. In 1969, shortly after the events of BioShock 2, the disappearance of Sofia and Eleanor Lamb brings about a violent, chaotic conflict in the whole of Rapture, as the Splicers return to a battle for survival. However, the collapse of Fontaine Futuristics and Persephone into the trench below caused a chain reaction within the energy mass inside, and at this point it erupts, creating a powerful upward current and bathing the city in energy. This has the effect of temporarily sating the Splicers' ADAM addiction and reversing their insanity. Driven by a need for escape, they empty the buildings and sever their foundations, riding the current to the surface. These refuges then proceed to drift across the entire Atlantic Ocean, and some of them land on various different coasts. The surviving Splicers then proceed to establish miniature, isolated communities although a lot of these revert to a Rapture-like state of conflict as the denizens return to their feral state. The largest of all of these settlements, formed by the survivors of the Proving Grounds tower, is New Rapture.
Backstory II: Rebirth
Located on the American East Coast, New Rapture manages to remain unseen thanks to a cloaking field created out of Rapturian technology. As the citizens settled, they also started to procreate with the help of their remaining ADAM stocks. This has two effects on its children: on one hand, they mature at the same rate as Jack, and on the other gain a Plasmid affinity (and thus an addiction) since birth. They are also born deformed in a way similar to their parents. Resentful of their heritage, the children of Rapture turn against their weakened parents, and commit what is known as the Great Purge, which lasts from 1972 to 1975 and culls approximately three-quarters of New Rapture's "old" population. However, they are stopped as a charismatic figure rises to power and puts an end to the infighting, promising the entire population "glory and their just reward". This man is Cassius Blaine. After assuming control of the city, he gears the city into full production and militarizes the population, until the city rivals the old Rapture in size, power and technological advancement (relative to its age). This lasts for five years until 1980, which is when you come in.
1980: BioShock 3
After drifting in the Atlantic for twenty-two years, Jim's bathysphere washes up on the coast of New Rapture. Thanks to the ADAM he had consumed, Jim awakens fully healed of his injuries, although completely drained of his powers. Stumbling into New Rapture, he is attacked by the population and, after holding out on his own, is contacted by a secret organization under the command of Dr Tenenbaum, constituted mainly of grieving mothers, who work against Blaine's regime to try and recover the new Little Sisters, their children. Although initially distrustful of Jim, as she recognizes him and recalls his past as one of Ryan's henchmen, she puts her hatred aside and orders him to find a way to kill Cassius Blaine by opening up his fortress in the middle of the city, guiding him through the city with the help of some of her assistants. His other two guides are Giles Hendrickson, a sympathiser to Tenenbaum's cause and the one who first found him; and Claudia, one of the mothers in the organization. Together they help him survive in the city, and give him different moral options to choose from.
Warning: Nonexistent spoilers ahead
Towards the end, it is revealed that Claudia is, in fact, Laura, who had been working for Cassius Blaine all along. He also granted her immense Plasmid powers, akin to that of a Big Sister, and implanted a mind-control device within her, although she believes she is serving him willingly. In a display of her power, she destroys Brigid Tenenbaum's hideout, killing the doctor as well. In her final moments, Tenenbaum puts her plan to action, and shorts out the power across the city, opening up Blaine's fortress but also momentarily disrupting the city's cloaking field. Jim then proceeds to enter the citadel, and discovers that Blaine is in fact creating a Plasmid-powered army to invade the United States. Within, he encounters Laura, now aware of Cassius's mind control on her, who unwillingly engages him in battle. After winning, the player can choose to spare her life and reignite their old flame, or execute her in cold blood. Jim then proceeds to storm Blaine's defenses. Depending on the player's actions, Jim can either receive assistance during this batttle, or be granted immense Plasmid powers to use on his own. Finally, he finds Cassius Blaine who, in addition to fuelling his army with ADAM, had been using the stuff to turn himself incorporeal. His brain is stored in a giant vat, and is the size of a Big Daddy, and his "human" form is both nigh-omnipotent and indestructible, as it is simply a projection of his mind. However, Jim destroys the vat, apparently destroying Blaine for good. However, as Blaine's mind was controlling every minor function in New Rapture, the city collapses and Blaine's citadel eventually self-destructs, producing an explosion of pure psychic energy and annihilating the city. Meanwhile, Jim escapes the collapsing fortress and tries to make his way towards the city outskirts. Depending on the player's choices, the player may or may not survive the blast. If he does, however, he will be rescued by a group of US Army soldiers dispatched to the location after spotting the city during its power outage, and will leave the city with or without Laura (whether she's alive or not). However, Cassius Blaine doesn't completely die, and his ghost prevails along with some mutated survivors in the ruins of New Rapture...