The Champions Universe is a completely different world from ours yet some smiliarities exist. This world also has a Next Gen even though it may differ from the one in Paragon City. The people of this dimension might be aware that the COH Universe existed but they aren’t from it and have their own story.
Same as Different Dimension but this world’s Next Gen was actually founded by member of Paragon’s NG that have fled through an immensely powerful portal to escape the failing reality cluster around Primal Earth. These are the same characters, stranded on a new world, trying to rebuild.
Millennium City Moving Company :
Paragon City was destroyed in a terrible event but the Next Gen branch in Millenium City survived. Yes this one claims we are still in the same world, just moved to a different city.
Next Gen’s original timeline was one in which mutants and humanity waged a terrible war. But they traveled back in time, rewriting all of history. People lived completely new and different lives. Now they pay the price for their hubris and reality rewrites itself again. The Champions Universe is not a new world. It is our world but the timeline has been rewritten. Some people are the same, some are not. This would be along the lines of reinventing ourselves in the way of storylines like X-Men alpha or Age of Apocalypse.
Gal or Dayrunner manage to make the transition(along with a substantial/most/all of the NG staff/peoples), along with a big chunk of tech. However, the changing of realities(not just dimensions, since the multiple portal corp dimensions were all one super-reality that was CoH) drained most of the members, but left Gal/Dayrunner/Lightnyng/whoever 'awake'(probably whoever pushed the portal button) long enough to find a CO Grim(could even be CoH grim) and explain that, at the very least, it's terribly important to protect this stuff from her Sister reality. Also, she now has access to a big chunk of escaped tech, except only about 30% of it works, and of that, she has no idea how to use it! The rest of the group is put into a sort of rejuvenation pod that keeps them alive and stable while they recover, adapt, etc. to the new reality. Of course, anyone who wants to start fresh could simply make a new version/alt of the former mutant, and the CoH-version is just asleep in a pod. Which could be fun when the original wakes up....
Interdimensional Space riders:
Gal/Dayrunner/CoH Grim/etc. create a base on Mars/Moon/Pluto/Asteroid ala Magneto's space colony-thingy after arriving from CoH-verse. They then slowly release NG members from cold sleep and help them adapt to a world with less mutant hate, No freedom phalanx, and weird ugly bug people instead of Rikti. At the same time Purgatio could do the same as well, so we could bring villians too yay! Co/CoH grim is made leader of a new NG in Detroit(since it fulfills the same basic geographic location as Paragon does), which is about the same as the old one. Someone using a front-company that makes money off of smart investment in mutant heroes/etc. while secretly being a dimension-hopping/future-tech shadow organization. And Grim would still be the leader, just with shadowy overmind characters that you don't get to see cause Tbirdy and Gal like to nap a lot!:P
“Listen to the mustn'ts, child. Listen to the don'ts. Listen to the shouldn'ts, the impossibles, the won'ts. Listen to the never haves, then listen close to me... Anything can happen and anything can be.”