Future Serenity

Possibilities are:

The Alliance Campaign
PCs are Alliance military, probably the crew of a small patrol ship, trying to be the good guys working for the corrupt and oppressive Alliance. I ran a delve for this idea, Cargo of Misery. It did not quite work out the way I hoped, although we did all have fun.

Tradewar
This was one of the themes that I didn't fully explore in The Yellow Submarine Campaign. It expands on the corporate rivalry between Oberlindes and Tukera and will draw heavily on The Traveller Adventure campaign book for Classic Traveller. PCs would be the crew of a freighter, probably a larger one that they may not own themselves, maybe an Oberlindes Lines ship.

Deadliest Cargo
Emily suggested this one night while watching Deadliest Catch. It's another tramp freighter campaign, focusing on the rivalry, pranks and competition between a couple of ships. Some of the NPCs (and some PCs) might be down on their luck losers. It could be part of Tradewar. We did a few delves to try it out; see Boon Companions, Reaver Detour and Cash on Delivery. We also discussed Deadliest Salvage, the characters are a deep space salvage crew.

History
A campaign set before the Firefly show, maybe during the war, maybe long before hand. Got some thoughts about the Pre war period here.
Update: We recently did a war flashback adventure with new characters, Stories from Serenity Valley.

CyberSerenity
A cyberpunk campaign on the Core Worlds of Londinium, Ariel, etc. It might run during or after the Yellow Submarine Campaign and could lead to the Second War of Independence as the Core Worlds rise up against the corrupt Parliament.

Serenity Bebop
Cowboy Bebop style bounty hunting in the 'Verse

Then I have some themes that could be combined with one of those. Both of these change the canon setting of the show drastically, although I think recontacting Earth is less canon breaking.

Earth-That-Is
The Alliance's history of the exodus from Earth is not quite accurate. An embassy ship arrives from Earth to invite the lost colonies to join their Confederation. But they do not approve of the Alliance…

We are not alone
Why is the Alliance fleet so damn big? Why do they need monster ships like the Longbow cruisers and the Crete carriers? Because there is intelligent alien life, and they are not friendly…

The Big Damn Heroes book gives some ideas, such as:
The Dressler Report
The Dressler report is a secret study about the future economic failure of the Alliance. Supposedly it has been suppressed and the author is on the run. The player characters get involved in the search. This is a possible CyberSerenity theme.

Orbital Underground Railroad
The characters are people who specialize in helping dissidents escape the Alliance and settle on new worlds. These are the people who helped Simon rescue River.

Skyplex Nights
The characters are based on a skyplex instead of a ship, which gives more of a Deep Space 9/Babylon 5 theme as the adventures come to them.

Secrets and Ideas
The Yellow Submarine Campaign involved several secrets: following up on the Miranda Broadcast, the location of the HMS Seeker, the survival of The Butcher and Admiral Sharpe's crew. Big Damn Medics focuses on Ru, another person modified like River and touched on organlegging. In trying to come up with a new campaign idea, I have looked at the episodes for themes and suggestions, basically looking for adventure seeds:

Serenity (Pilot): Reavers, River's creation, derelicts and illegal salvage
Train Job: Niska's empire, drug diversion, terraforming spawned diseases
Bushwacked: Reavers, Fed patrols, failed settler ships, derelicts and illegal salvage
Our Mrs. Reynolds: Saffron's past, ship jackers
Out of Gas: Why did Inara leave the Core? Crooked deep space salvage crews
Shindig: Terraformers use slaves and so does high society, duelling
Safe: Book's history
Ariel: River again, Hands of Blue
War Stories: Niska again, psycho philosopher Shan Yu, River's skills
Trash: Saffron again, biological warfare, other Browncoats (Monty), Earth-That-Was artifacts, Bellerophon's floating estates
The Message: organleggers, corrupt feds, blastomere organs
Jaynestown, Heart of Gold: How do these petty warlords end up in control?
Objects in Space: Jubal Early, bounty hunters, River's ESP
Serenity (Movie): Rent a cop rim security, reavers' creation, Operatives, poorly terraformed worlds, who was Mr. Universe hiding from? Who built the base? Why was it abandoned?

New Ideas

I have recently been trying to think of new ideas that were not inspired by events in the TV show and movie. I'm trying to come up with new ideas for things that could happen in the 'Verse, in other words to "think outside the box-set". So here's a couple of new ideas, staying in the "former browncoats with a freighter" theme:

Lost Sheep
The characters find a clue that leads them to believe that Browncoat POWs are still illegally imprisoned and they try to discover what happened to the missing soldiers, who include some early heroes of the war. EDIT- We ran this campaign from January 2014 to March 2016.

Traitors
The Independents' defeat at the Battle of Sturges opened the way for the invasion of Hera and the end of the war. How did the Alliance find the fleet rally point at Sturges? The player characters include some former Blackjacks who discover a clue that may lead to finding out who betrayed the Independents. This one is a bit weaker though, because the whole campaign is "Find somebody and revenge-kill him".

Trading in Danger
The title is stolen from Elizabeth Moon's "Vatta's War" series, the campaign would deal with a freighter crew during the war. The crew would probably be neutral, just trying to make a living and not take a missile from either side. Or they could be part time smugglers.

NEW- Runaway
One of the crew is secretly a runaway from a wealthy and influential family in the core. They are pursued by bounty hunters, both from friends and foes. Then something happens and the PC becomes the sole heir