Hi.
Sometimes I think it is really interesting to see events from another character's point of view, especially if that POV is sufficiently different from the original characters - and even more so if their morals differ as well.
I haven't had the opportunity to read anything of yours, but from your post I gather the work concerns lions?

Events as seen from the pride alpha would be very different to those seen through the eyes of a rival male or a female.
I agree with your suggestion about back story; it is also something you could use in the parallel series - you could expand on any historical points you raised by having them observed and participated in by the characters rather than just as anecdotal points.
I think one of the main things to be wary of would be maintaining a strong plot/suspense structure that doesn't rely too heavily on the original. The readers need to be immersed and surprised by events, even if they already know that they are going to occur. Maybe this could be done by having those things happen on the new character's timelines at incredibly inconvenient times?
Any scenes where a character without a POV in the original has to track, hunt or pursue something could be handled quite nicely in a parallel story. For instance, if in the original the antagonist suddenly appears to try and thwart the protagonist 's mission, in the new story that antagonist's journey to get there on time, any detective work they needed to locate them, and any trials they faced on the way, will be completely new and fresh to the reader.
I do think, though, that if the new work does concern antagonists rather than allies, that you should make their motives solid and thus let those characters be perceived as misguided protagonists in the new story, to engage reader sympathy.
I hope this all makes sense and I am not rambling too much.
I think your idea will be as good as you can make it! It sounds very ambitious to me, but that isn't a bad thing at all.
One last thought - if your story is about lions, and the events seen by them, how about having the parallel story from the POVs of another species? An unlucky herd of antelopes, a hyena pack, a pair of vultures who follow in the pride's wake, or an eagle watching the events from high above?

just a random thought. Even if it isn't what you're looking for, maybe that would be good fodder for parallel short stories (or exercises to relieve writer's block?) or something.
Good luck!