So I am going to run a GURPS campaign, still quite a ways away, but I am going to use this thread as a way to organize some of my thoughts and put stuff that is general player knowledge up.
The campaign multiverse is a modified form of the standard GURPS infinite worlds setting, there are two primary cross dimensional organizations that are reasonably friendly with one another and act as protaganists and there are a few others that are generally antagonistic to them. Player characters can either be from one of the two protaganist organizations or they can be people from one of the many planes those organizations visit who has been recruited, swept up, or brought along by accident.
The protaganist organizations are infinity unlimited, a company that has discovered cross dimensional travel using technological means who now works with department of the UN to try to keep order, of a sort, across the multiverse, and the invisible college, a hidden college of magic that teaches a wide variety of traditions and is able to travel through the dimensions. The two factions are quite aware of one another and do not always work to the same ends but are both generally benevolent. The antagonists that both are aware of include the Reich, Nazis who have mastered planar travel, the cabal, a rather more diverse and somewhat more sinister group of mages than the invisible college, and the swagmen, dimension jumping con artists and swindlers who use their ability to change planes purely for their own betterment.
The commonly known worlds, at least among planar travellers include the following.
Homeline, also known as Canada, this is the base of operations for infinity unlimited and as far as they are aware the only plane on which projector technology works. It is called Canada by those from other dimensions because the Infinity Patrol's base is in Alberta and that is usually the only part they see. It is a no mana plane, TL is early 9/ late 8. The world is very similar to the one we are familiar with, up until the development of cross planar travel, that was a couple decades ago at this point and is something pretty much everyone is aware of, but most people have not taken part in.
Assiah, sometimes called Venice, the home plane of the invisible college. This world is in the enlightenment era, similar to our familiar world it includes a race of sentient fish men, who live in relative peace with humans. Physics are different here and technology above TL 4 does not function, this means that the conveyors that Infinity Unlimited use cannot get out if they have gone in. The Invisible College is headquartered in Venice, thus the name. The world is low mana, with the college occupying a pocket of normal mana.
Reich, Germany, or Deutschland is the world of the Nazis, they were victorious in the second world war and moved on to consolidate their wins and discover cross dimensional travel. Their methods are not as refined as infinity's and is not something most citizens, or the fuhrer, are aware exist. The world is roughly the same TL as home line, extermination camps are not commonly seen, since their work is mostly done, but a few still exist. No Mana
Zebu, A world in what seems to be an endless mideval era. Technology does function here, although sometimes unreliably. It bears very little resemblance to the world we are familiar with, with different geography, languages, and so forth. The fantasy races people are familiar with are here, elves, dwarves, orks and so forth, as well as the strange magical race known as glurons. Normal mana, the world is considered a barbaric backwater by both infinity unlimited and the invisible college, but things keep happening there with potential consequences beyond the borders of the world. TL 3
Redemption, A world that at first look seems to closely resemble ours in 1884, however there are an awful lot of strange things going on. Schools of ritual magic wield real power, including the traditions of America's native tribes and physics seems to be subtly different in ways that allow ideas that turned out to be wrong in our world to work after all. Early TL 6 Normal mana but with quirks to the magic system.
These worlds all have a certain gravity, random errors that throw travellers to a random plane seem to end up on one of them more often than other places and they also seem to have a higher proportion than most of travellers born there of planar travellers. The knowledge archives in Infinity's research department and in the library of the invisible college include many more worlds which have been explored and categorized, but these are the ones that most who have travelled between planes are aware of without further research.