The Bureaucracy
Nobody remembers exactly in which year the Great Snafu took place, but people generally agree that it was on a September, or perhaps on a Saturday afternoon. Also, it involved blowing up the Universe, which made pretty much everybody unhappy, except for a few people who had been waiting for this opportunity to loudly exclaim "I told you so", and even they were not happy for long.
So, when the Universe was rebooted "with a 99.999% confidence value", the House of Smiling Hands was barred from Time Travel indefinitely and the Agency for Preservation of Space-Time Continuity was created. Brave Agents dashing around time and space in their Continuum Indirections, fighting off mad scientists, resolving the Y2K bugs before they could overwrite the Universe, bodyguarding baby Adolf Hitler and generally maintaining the status quo.
All this took place (subjective) eons ago. Nowadays, the Agency is known as the Time Bureaucracy. With (subjective) years, administrations and fashions, the Bureaucracy has reinvented itself countless times. It has been a strict-but-efficient police, as well as a dusty museum of inventions past and future. It has become a travel agency for dignitaries, as well as a time-traveling gossip source. It has been the military arm of an everlasting dictatorship, as well as an encyclopaedia of entirely verified facts. It has been a time-agnostic anarchist commune, as well as a an undercover channel used to buy future technologies without having to go through the messy process of research. It has been used as a torture chamber and as a taxation office. It has been public and secret, fashionable and forgettable, progressive and repressive, pangenicist and eugenicist and pretty much every other combination.
The Enemy, Sort Of
Throughout its existence and despite all these reinventions, the Bureaucracy has devoted and continues to devote considerable efforts to fighting the main threat towards the continued existence of the Universe.
This threat is, of course, every single past, future and alternate versions of the Bureaucracy. Because, well, they are so very wrong, aren't they?
This is a conflict of surprisingly little violence, made of subtle manipulations and grand gestures, of infiltrations, desertions, propaganda, and paradoxes. A Cold War more than a battlefield.
Welcome to Space·Time!
Ronin Time Bureaucrats
Unsurprisingly, with this Time Cold War, Bureaucrats tend to disappear here and there. A few died, surely, in the line of duty. Others switched allegiance. Some even survived the erasure of their entire timeline. As for others, well, they just decided to go their own way, out of boredom, disgust, or on their own personal quests. Once a disappearance is found out, the Bureaucracy searches for its missing Bureaucrats, of course. But, well, Space·Time is a large place, and it’s hard to find someone who may have accidentally misplaced the transponder from their Continuum Indirection and sent it hurling towards a black hole.
That’s who you are, by the way. A runaway crew of Ronin Time Bureaucrats, in your Continuum Indirection, flying merrily away from the Bureaucracy and towards... well, towards all of Space·Time!
So what if past/future/alternate versions of the Bureaucracy (and possibly yourself) are looking for you and/or greedily rewriting the Continuum while you're away? It's none of your business, right?