It would start in a new reboot "Earth Prime", but the multiverse itself would be the same one we all know and love, even if they don't go to the same worlds.
- ...Which actually already happend in a certain episodes where they came to a world with a "Sliders"-style TV show. which means that there might be more worlds with "Sliders" show, and at least one that survived longer.
- A universe where the Kromaggs never took over the show and it lasted ten seasons would be pretty awesome...
It's likely that there are a fixed number of dimensions you're likely to slide into. Of course this also means that losing or gaining a member might very well decrease your chances of getting back to the original dimension.
In "The Breeder" the alien creature could in fact have been an alternate universe form of Goa'uld and behaves in a manner similar to Hathor. In "The Last of Eden" the cannibalistic underground Morlock type creatures bare an external similarity to the Wraith. The latter episode also makes references to a group of Gineers (engineers; precursors who'd left the people with advanced technology to take care of their needs but without the knowledge of how it operated). It's possible these Gineers were in fact an alternate form of Ancients.
Almost everyone speaks English the exact same way no matter where they are (no matter how different other parts of history may have been the development of language never is). Both series also revolve around wormholes for their primary form of travel and the same "rules" of interdimensional travel apply (like that you'll probably end up somewhere close enough to your own world that all the same people exist, even if some of them have died and it's different enough to have the majority of the population wiped out).
The reason why no one seemed to notice the drastic character change in Maggie between the two seasons is because there wasnt one. The Sliders from season 4 onwards were a completely different group of people from the original Sliders. They started out on a world very similar to Earth Prime (which, being their world, they called Earth Prime) and just as there are parallel worlds they were parallel Sliders.
Their version of the original four got lost in the multiverse and travelled to several worlds which were similar to the worlds visited by the actual original four (effectively their slides were offset or parallel to the slides of the original cast). Their Arturo died along the way just as ours did. They met their Maggie but she was a much more likeable version.
When Season 3 ended with Wade and Rembrandt on Earth Prime they really were on Earth Prime and it was never invaded by Kromaggs. The last we saw of the original Quinn and Maggie was them in a futuristic Earth where they were able to acquire the technology to safely and easily return to Earth Prime.
Due to the lack of conflict or drama for our heroes now, the show therefore switched between seasons to another group of Sliders to continue their adventures for the rest of the show. These Sliders were very different, with Quinn being born in another dimension and Wade being the type of character the writers would sentence to such a horrible fate.