I came up with my own Civil War plot, just because. Probably more Spiderman heavy than is possible at this point and it's incredibly rough I thought it all up in like an hour. I still like the basic idea:
Starts out with a question time esque debate about the newly instated Superhero Registration Act. Tony supporting it, Cap opposing of course. Wakanda has gotten involved so T'chala is there, also opposing the act. Since the events of the first Avengers more and more superpowered vigilantes have sprung up. Spiderman has become like the iconic vigilante. The plot revolves around Cap and Iron Man trying to sway them to their side. If Stark can get the Iconic vigilante hero to support his act, it will gain a lot more traction.
Early on in the film the supervillain Nitro (http://en.wikipedia.org/wiki/Nitro_%28comics%29) is attacking New York (he's the guy who sparks off the original civil war, though he's in a different role here. But it would be a nice reference). No backstory for him, he's just there blowing stuff up, to really establish this atmosphere that superheroes and villains have become an everyday occurrence. Cap and Falcon are fighting Nitro, and then Spidey shows up as well. Then Iron Man and War Machine with a load of SHIELD Agents turn up. The three groups can't work together so Nitro escapes. Some harsh words are exchanged between Cap and Stark.
Later we get another fight between Iron Man and Nitro. The fight culminates in Nitro being captured within a pocket dimension prison, created using technology derived from the Tesseract. IIRC this is another reference to the original arc.
Things escalate between Cap and Stark and Stark comes with SHIELD to arrest him. There's a tussle at Cap's home, he calls in Falcon and they manage to escape. Pretty much exiled, the two of them set out to find the Winter Soldier, partially because Cap was already on his trail and being exiled is a good time to look, and partially so that he can help them take on Stark's increasingly totalitarian regime.
Meanwhile we get some montages of Stark and SHIELD apprehending superheroes. Spidey turns up in Stark's office hacking into his computer. He's looking for information on his parent's deaths, who were SHIELD operatives back in the day. Stark offers to help him out in exchange for supporting the SHRA. Spidey acts coy and vanishes.
Cap and Falcon find Bucky, they bond somewhat even though Bucky is still having trouble remembering his old life. They make their way back to NY from wherever they where to confront Stark. First they track down Spidey in NY and try to persuade him to side with them. He's almost persuaded but suddenly SHIELD tracks them down. Spidey once again vanishes, reluctant to get involved in the conflict. Crossbones and War Machine attempt to arrest the trio (Crossbone's involvement is another reference to the original, in which various villains are hired by Stark to capture heroes). Cap escapes, but Falcon is killed in the action and the Winter Soldier is captured.
Turns out the Winter Soldier killed Peter's parents. This is the information that leads Spidey to agree to side with Iron Man. He unveils himself as Peter Parker on live television, and the SHRA gets a lot more traction. Spidey helps track down and arrest more vigilantes. But over the course of events we can see that he is rather unsure of Stark's methods. He's ultimately just a kid caught up in something way too big for him.
Cap infiltrates SHIELD in order to free Bucky, who's been put into a pocket dimension. Cap manages to save Bucky from the prison, but his actions inadvertently free Nitro as well. The ensuing scenes are absolute chaos, with everyone trying to kill/apprehend everyone else. We get a final confrontation in which Cap, Spidey, Stark, Winter Soldier and War Machine eventually team up to take out Nitro. Things are looking bleak but the cavalry arrives in the form of T'chala, in his Black Panther suit and he manages to turn the tide against Nitro. The fight brings back some good feelings between Cap and Stark, who realises his methods had become totalitarian. They part on reasonable terms, but can't truly be friends again. Spidey is disillusioned with both - Cap for allying with his parent's killers, and Stark for pretty much using him as a political pawn. He leaves to pursue his own path.