After I finished running the EotE beginner set for my group, we were all hooked. I came up with a homebrew followup campaign to run next, which we just finished. Not sure if anyone is actually interested in writeups of other people's campaigns, but here we go anyway. Sorry for the wall of text!
After finishing Long Arm of the Hutt, the players were approached by Maru Jakkar, the Black Sun woman. She collects works of art done by heinous villains, and has recently acquired a portait painted by Tarkin. She's after her next prize, and wants the players to help get it.
She tells the players that Darth Malak, from KOTOR, was an accomplished sculptor before becoming a Jedi following the destruction of his homeworld. While in the Unknown Regions with Revan, he commissioned the construction of a massive battleship called the Colossus that would be his flagship during his invasion of the Republic. The Colossus was not completed in time for the invasion so they attacked without it, but Malak had them install a prototype jump drive that he could use to summon the vessel to him when it was finished.
Fast forward to today, and Jakkar's network has detected the jump signature of the Colossus. Someone figured out how to jump it from the Unknown Regions to somewhere in the known galaxy. Jakkar hires the players to find the Colossus and recover one of Malak's sculptures from its bridge.
There's a catch, though. No one knows where the Colossus jumped to, only that a bunch of sensors detected an anomaly. She gives the players a list of six facilities that have the sensor data, and tells them they need to get 3 data points so they can triangulate the Colossus's position. The six facilities were:
1. A secret Industrial Automaton facility built into an asteroid near Hoth [where the droids have gone amuk and killed all the scientists]
2. An Imperial early warning station at the Kuat Drive Yards
3. A Gand Corellian Corvette called the Rendilli Star traveling the Hydian Way
4. A Hutt weapons lab researching cloaking technology on Nar Shadaa
5. A Guardians space station in the ruins of Alderaan
6. A university on Devaron [which is currently engaged in a civil war that the Empire is intervening in]
7. An Ithorian herd ship in orbit over Ithor [they would have just handed over the data, but the players thought nothing could be that easy and suspected this would be the hardest option]
The players went to Devaron first, where they talked their way past Imperial patrols, survived an orbital bombardment, and then fought an ISB agent who was also after the sensor data.
Next they went to Alderaan, where the Guardian station was under attack by a Sith cult also looking to find the Colossus. They fought their way in, and managed to retrieve the data as the station was blowing up around them.
Last they went to the Rendilli Star, where a Gand functionary framed them for the murder of his boss, who he felt was holding him back from achieving greatness. The players solved the murder and got the information they needed.
WIth those 3 data points they calculated the Colossus's position (they actually did the math, I just gave them raw numbers on the intensity of the power reading at each location). They arrived to find it in ruins (the jump blew it up), and a Star Destroyer already picking through the wreckage. This was a dungeon crawl, and they fought their way through the Colossus' interior towards the bridge. During the fight a Sith cult warship arrives and engages the Star Destroyer. The players use the Colossus's weapons to try to keep the balance even so the Sith and the Imperials pummel each other without gaining the upper hand (I used some of the mass combat rules from Onslaught at Arda for this).
Eventually they reach the bridge, where they met the leader of the Sith Cult. The leader was an actual Sith, who attacked them with a lightsaber. One of the players gets 3 advantage and shoots the lightsaber out of his hand, and another player grabs it and cuts the Sith's arm off. The Sith Force pushes everyone down and flees. The players grab the sculpture and return to their ship.
The players fight their way past the screening TIEs and jump to light speed. Maru Jakkar pays them handsomely and offers them another job. Campaign over!