I grew up with Quantum Leap; it's one of the first shows I remember with recurring TG elements. It left me with an abiding fondness for the concept of mental time travel, in which someone travels back (or forward) in time by possessing someone in the past. For that reason--and because I love period costume!--I'm launching the Chrono Corps universe, a new open universe that anyone else may write in if they're interested.
The Chrono Corps is a secret intergovernmental agency in the near future, devoted to using time travel for the betterment of humanity. Chrono Corps agents travel back in time for a variety of purposes, such as research, scouting, combatting rogue time travellers, and "putting right what once went wrong."
The exact goals of the Chrono Corps can sometimes be difficult to fathom, even for their agents, but the CC can nevertheless be considered the "good guys" of time travel. There are, however, other organizations that use time travel for more sinister purposes, as well as rogue time travellers who don't belong to any larger organization.
CC agents travel back in time using a machine called the "Conduit". The Conduit projects an agent's mind into the body of a person in the past. The consciousness of the host body is entirely suppressed while the agent is in his or her body, although he or she will have vague memories of having lived through the experiences that occurred while he or she was possessed.
The Conduit is typically capable of pinpoint accuracy when sending agents into the past; it can place them in a specific body at a very precise point in time. Mistakes are possible, though... and more frequent than the CC would like to admit.
There's a strange quirk with the Conduit technology: agents can only be placed in a body of the opposite sex. If an agent is placed in a body of the same sex, the body spontaneously combusts, killing both the agent and the host instantly. (In fact, all documented cases of spontaneous combustion were actually the result of early experiments with the Conduit.) No one knows why same-sex possessions are fatal, but it seems to be an inviolable rule of time travel.
Agents may be sent back either solo or in small teams, depending on the needs of the mission. New agents are often assigned a mentor, a more experienced agent who trains them and accompanies them on their first mission.
Agents are linked to the Conduit by a "neural interface", a sort of mental computer program that can be brought up at will. The neural interface contains an extensive historical database to assist agents with their missions. The database reflects the "current" history, meaning it instantly changes when an agent changes history. Agents on scouting and research missions can edit the database, allowing them to record any new information they uncover during their mission.
Information in the database is compiled from the historical record, as well as from scouting and research missions. The database is limited to information the CC can access, meaning there are sometimes considerable gaps in the database. The database, for instance, records the names of most of the pharaohs of Ancient Egypt, but it doesn't include the names of Ancient Egyptian commoners, nor does it include those of certain pharaohs whose names have been lost to history. An agent could, however, theoretically travel back to Ancient Egypt in order to recover the missing names.
The neural interface also serves as a translator. An agent who possesses someone who speaks a different language will acquire the language skills of the host. To the agent, it seems like they and everyone else is speaking the agent's native language, but they are in fact speaking the host's language. The same rules apply to written language. The translator also "corrects" the agent's accent, meaning that, for instance, an American agent who posssesses an British host will speak with an British accent.
There are some interesting drawbacks to the neural interface's translation function. Because the translator is tuned to the host's native language, it's possible that an agent will be unable to speak his or her native language. For instance, a French-speaking agent who possesses an Urdu speaker in the recent past will be unable to read, speak, or understand French while possessing that body. An agent who possesses the body of someone who's illiterate, meanwhile, will lose the ability to read or write, even in his or her native language. (Note, this does not apply to the database in the neural interface; agents will always be able to read the database and, on scouting and research missions, contribute to it.)
Most importantly, the neural interface explains an agent's mission objectives and shows whether or not those objectives have been completed. Agents can only return to the present once all objectives have either been successfully completed or irreversibly failed. Until then, agents are trapped in the past.
From the perspective of someone in the present, agents return immediately after they left. An agent may spend a decade in the past, but to the technicians operating the conduit, the process only takes seconds. While this certainly makes long missions much easier, it also means that it's impossible for agents in the past to communicate with the present. Agents are on their own when they're in the past.
If an agent's host body dies, the agent's mind dies along with it. There's no way to retrieve the agent's mind from a dying body. Should an agent die in the past, all neural activity in the agent's body will cease immediately after the agent is projected back in time, and the body's other vital functions will cease soon afterward.
Some agents, for one reason or another, choose not to return to the present. There are also rare instances in which the Conduit glitches and its connection wtih the agent in the past is severed, leaving the agent permanently stranded in the past in an unfamiliar body. In both these cases, the agent's body, again, dies immediately after the agent travels into the past.
It's theoretically possible for agents to travel into the future using the Conduit, but it's a difficult and dangerous process. The CC has no record of the future, which means the neural interface's database and translation function are useless. More importantly, it's virtual impossible for the Conduit to pinpoint a host body in the future, since the CC has no record of who is alive in the future. That means agents who travel into the future are essentially placed into a random body in a random place, which is incredibly risky.
One final note: these rules are all flexible. Please don't feel bound to them. Bend them or break them as necessary. In my opinion, the rules of an open universe should be flexible enough to enough to allow a writer to tell whatever story he or she pleases. The rules are merely a starting point. So just be creative, and have fun!
Hope to see someone else pick this idea up. :)
I'm certain I've forgotten something. If I remember more stuff or think of new details, I'll add them later.