I'm definitely not doing a Doctor Who style. I would do a Time Travel Stat NES, but I'm having trouble coming up with a good ruleset for it. What's I'm asking about now is Story v.s Stat NES partially, and how to implement each.
EDIT: I'm also going to come up with various premises and see what people think of them. Some bits are in slashes, as they can be done various ways.
Since a Story NES isn't that much work, I may as well try both a Story and a Stat NES. However, I'll have to find an appealing premise for both first.
Idea 1: Clash of Ideologies
Earth is an obscure planet on the edge of the universe. It is primarily relevant because of a bizzare quantum anomaly, which draws time travellers to the planet around the year 2013 and traps them there. They can still time travel within Earth's history, but there's no way back for them.
Equipped with advanced technology and knowledge from Earth's own history, these aliens attempt to change Earth's culture. Some wish to take power for themselves. Others wish to do what they believe is right. Some sit back in their Temporal Storage units for fear of their lives... but they're not part of this game, mostly.
(NOTE: In this version, extreme Butterfly Effect would be in play. I'd consult with historical experts in the NESing forum who aren't actually playing in order to get as plausible an outcome as I can. Butterfly Effect can be used to undermine your opponents in other time periods. The aliens don't have Ripple Effect Proof memory, but do have records of previous timelines on their computers stored automatically.
You would be able to compensate for opponents undermining what you're doing, however. First- you create contingencies for your characters to dictate how they might act if the timestream has come out from under them. Second- you have acess to Temporal Storage, a sort of suspended animation where agents can look on the time stream before going in. Agents can still be killed in the points of the timeline where they are, however. Third- time travel backwards takes Chronoenergy, and more Chronoenergy the further back you wish to travel.) Fourth, of course, you can alter events to save your agents.
Everybody has the ability to disguise as a human, and automatic ability to understand any Earth language they bother to take from their database).
In the event of a paradox, time becoms Circular. Events fluctuate update by update between the two possibilities until player actions remove the paradox.
Idea 2: The Corruption of Power
Earth, 2013, Meran City, U.S. The side-effects of a scientific experiment lead to large numbers of people gaining a mysterious form of time travel. This allows them to mentally travel on their personal timelines, seize control from their younger selves (who are still aware and conscious of what's happening), and set events on a new course.
But power corrupts, it is said. The power these figures wield is enormous, and new. Their memories may be Ripple Effect-Proof, but their bodies aren't. Can these once ordinary people use their powers responsibly, or will they be a blight upon the world?
This one is intended to be as similiar to real Earth as possible (pre-time travel) except for the existence of the fictional Meran City in the United States, fictional state Meran. This way, players can have fictional versions of themselves easily slip in.
The idea is basically ordinary people, add time travel. However, these once-ordinary people are powerful enough based on their Time Travel to do extraordinary things.
Idea 3: War of the Psions
A bizarre quantum event transports large numbers of people from one Earth in roughly 2013 to another one, in 4000 BC. Despite the fact that the same mysterious quantum event gives them knowledge of at least one local language, most of the survivors die or fail to do anything of importance.
Those who manage to survive at least ten years, however, discover two second gifts. First, they don't age. Second, they can Time Travel...
This NES would play out mostly like a vanilla Fresh Start NES, except with one unique feature- Time Travel. E.P could be spent to travel back a number of Updates, whilst the Protagonist character is able to make a jump of 24 hours back in time once per in-game year. The Butterfly Effect exists, but to prevent headaches this version would have no paradoxes.
Technically speaking, there would also be a second unique feature- each Time Traveller gets to choose some facet of technological knowledge beyond 4000 BC's knowledge to keep for themselves.