Causing havoc on Earth is the first thing; once Earth and its defenses are crippled they will be vulnerable to a Klingon attack that Harrison will attempt to start.
Harrison serves under Weller whom in this timeline comes across the Botany Bay as opposed to the Enterprise. It becomes secretive and the Botany Bay crew is placed under wraps. This doesn't sit well with Harrison and is revealed in a flashback which is why the beginning starts out with Harrison at the hospital claiming he can save the child.
While the Enterprise is away on its mission at the beginning Harrison begins his attack on Earth, specifically Starfleet, with his former captain Weller trying to stop him. Harrison is victorious culminating with Weller's ship crashing in the bay.
Pike calls the Enterprise back to Earth because of the incident and to also discuss with him his actions concerning his track record as Captain. He is attempting to gauge Kirk as he is about to send him on a serious mission. Pike relays Intel that explains who Harrison is and after the ceremony for Weller’s Death Kirk and Spock go into detective mode.
Kirk and Spock locate Harrison and incarcerate him. Harrison is able to escape, and heads towards Klingon territory. Pike orders the Enterprise to pursue. The Enterprise is given some new crew members one of which is a specialist in genetics and has made some interesting discoveries concerning beta particles on the sub-atomic level and how they can alter organic material including human cells.
Pike gives Kirk Intel that Kirk then explains to the crew. Harrison was once a normal man but now has increased strength, smarts, and that he is now for some reason able to tap into the parts of the mind with telepathy. (This last power is one that helps his attack on Earth as well as him getting away from Kirk and Spock. The ramifications of what Harrison makes the crew do to each other in order for him to escape have caused friction amongst themselves forcing them to realize they can
trust each other and that what happened was not because of them but Harrison.) The Enterprise heads for Klingon Territory.
On Kronos Harrison has wreaked the same havoc he has on Earth with his new skill set. Because he is already there by the time the Enterprise arrives, it has to fight all the way causing poor Enterprise to be damaged very badly. The Klingons aren’t able to stop Harrison but they will not take any chances on the Enterprise. Kirk and crew make it barely and when they arrive they find Harrison attempting to depart. Kirk and company find the Klingons are trying to prevent his Harrisons escape also. They beam right into the middle of a fire fight.
Spock attempts to take on Harrison one on one but loses, Harrison escapes. Kirk is amazed at the decimation. They get back to the Enterprise and chase Harrison’s ship which is heading to a Starfleet outpost in a remote sector.
Harrison arrives to the secret location/Starfleet outpost where the Botany Bay’s crew have been kept. When he arrives he is notified that his presence is requested immediately…by Khan. CGI Khan advises him his work has been excellent but that he is no longer required. Khan attempts to have Harrison Killed to leaves no loose ends. In the process a machine that has been developed is aimed at Harrison which relieves him of his new found capabilities. He is now normal again. This same machine via flashback is the way Harrison became “super”. This outpost is a secret scientific Starfleet laboratory that Khan took over with the help of Harrison in the first place. Starfleet was hoping they could replicate the genetic superiority of Khan’s people without having to go through birth thing. That one could be normal, step into a machine and then have the capabilities instantly.
Back on the Enterprise Sulu advises they are approaching the coordinates where Harrison’s ship’s warp trail ends. Dr. Carol Marcus advises the crew she has been here before and breaks protocol in revealing she is aware of what was happening here but had no idea this was connected with Harrison in anyway.
They beam down to find the station empty and in ruins. Spock reads there is one life sign in the rubble. They find this life sign and discover it is Harrison who is not quite dead. McCoy is able to revive him and Harrison, now normal is regretful for all the damage he has done.
The machine is damaged and Dr. Carol Marcus is able to repair it for one more burst. Harrison offers himself to step in the machine in order to stop Khan. Spock questions this as he and the rest of the crew would like to know that Harrison won’t become mad again in the process. Harrison states that he won’t because of a little girl back on Earth. If he can do one thing right at this point it is to save her and he makes Kirk promise that if he succeeds Marcus will do everything in her power to replicate the machine and save this young girl from death.
Harrison steps into the machine and is back to supreme capabilities. He and the Enterprise crew head after Khan. Harrison reveals that Khan’s plan was to leave the Federation and the Klingons in ruin so he can once again rise to power and not just control a planet this time but the surrounding area of space with no enemies to combat him at home or abroad. With control of the entire area not even the romulans would be a match, especially if he is able to replicate the machine himself and create an army. Harrison believes Khan has another machine.
Khan’s stolen Federation science vessel the USS Reliant (which served the outpost which they just left is heading to Earth) Through Scotty’s miracle worker status he is able to get the badly damaged Enterprise fixed enough to be able to catch up.
Harrison relays if Khan has a second machine and if he isn’t able to take over Earth he will destroy it by causing an overload which would alter everything at the sub atomic level and would kill everyone on the planet. This overload would basically level then recreate Earth killing all life in favor of the machines distributed new matrix.
With this knowledge in hand the Enterprise attacks the Reliant but is no match as the Enterprise is already crippled. Kirk and company beam aboard the Reliant as through the fire fight both ships have their shields dismantled. As Sulu tries to keep the Enterprise alive, on the Reliant Kirk, Spock, and Harrison go after Khan. They make it to Engineering where Khan is at protecting the second machine which does exist. All 3 of them attempt to fight Khan but they can’t quite defeat him.
The Enterprise Reliant space battle has now put both ships in close proximity to Earth. Khan realizes he will eventually lose fighting Kirk, Spock and Super Harrison and sets the machine to overload hoping they are close enough to Earth. Harrison gets the upper hand on Khan and is able to kill him but all 3 realize they can’t stop the overload. Scotty can’t even get a lock on them because of the particle shifts throughout the Reliant. Spock states that if they drop the isolation doors around Engineering it should provide just enough protection from the particle shifts that at least two of them can beam out. At that point Spock volunteers himself even though he has love for Nyota he is a man without a world.
Harrison instead volunteers but makes Kirk keep his promise about the young girl. Kirk agrees. Harrison drops the isolation doors and is able to rob bridge control from the rest of Khan’s crew. The fire fight stops between the ships, Harrison and Kirk’s hands touch the glass right as they are beamed out and the Reliant goes to warp. Moments later Pavel detects the explosion just outside the solar system.
The Enterprise is home, months later in Space Dock looking a little more “familiar” after its repairs. Pike relays to Kirk that Harrison’s mother had a genetic disease that couldn’t be cured with conventional medical methods. She died and it somehow must have caused Harrison to do what he did.
McCoy and Marcus are waiting in a secure hospital area. McCoy asks if she thinks it will work. The doors open and this once dying young girl is now better and will have a chance at life. Dr. Marcus explains she can’t replicate the super abilities but she was able to reverse this specific girl’s condition through the data they kept. Through all of the explanations it is revealed that this girl and Harrison’s mother had the same disease. Dr. Marcus states that she found out she can do some other stuff with the data but that McCoy wouldn’t be interested as he isn’t into geology.
Rested, reassured and back together again the crew works on the refit of the Enterprise when Pike calls Kirk to let him know that space station Epsilon 9 was tracking an astronomical event that was so huge it measured almost an AU in size and is heading towards Earth. Pike shows Kirk what this event did to the Space Station and Kirk sits in awe. Kirk finds Scotty and tells him they need to speed up the refit. Due to the destruction that Harrison caused they are the only available ship in the area. Scotty explains how difficult it would be but then grabs his arm and says to Kirk that if any man can accomplish the tasks he has done then she’ll be ready for launch ASAP. Zoom out of the Enterprise in Space dock, the music starts up and the credits role.