How annoying would this be? (Next story idea)

Because I find myself absolutely incapable of not rambling, I've included a short version, and a long version ;-)

Short version:
Would it be terribly jarring as a follow-up piece, to have the perspective of a story "jump" from one character to another, say, per chapter?

Long version:
One of the concepts I'm already toying with, as an eventual follow-up to the story I've been working on is a retelling of events from another character's perspective.

I'm writing in first person, and I make no secret of my love of internal dialogue. I adore being able to really get inside a character's head and give the reader an insight into what the narrator is thinking of the other characters, as opposed to what they say or do.

With that said, though, I find myself eventually wanting to explore multiple characters' reactions. I can't really think of a good example without spoiling the surprises, so I'll just ask on principle.

Would it be terribly jarring as a follow-up piece, to have the perspective of a story "jump" from one character to another? Not every other sentence, of course. I could never do a proper third-person omniscient without utterly mangling it.

The idea here is that each chapter, or possibly a scene or set of scenes, a different character tells the story, probably based on who has the plot focus at that time.

It's going to be awhile, as I've taken the most dangerous vow a writer can utter: "It's finished when it's finished, and not a moment sooner" to keep myself from trying to rush anything, but I thought I'd throw this thought train out there and see what others think.

~Zoe T.