Why do you think Jasper also slept with Peter and Charlotte?
Because @theoriginalcarnivorousmuffin and I differentiate between fic and canon.
We write our thoughts on canon on tumblr, but in fanfiction we are free to make our own rules and have fun.
Lines become blurred, however (bullet pointing for legibility):
What we extrapolate from canon impacts the canon of our fics
Fun fact, therealvinelle only exists because people kept asking me questions about my choices in Nebuchadnezzar's Dream, and I thought replying to the same questions in the comment section was silly. So I made a blog, which became a beast unto its own. In other words, fic is impacted by how I view canon, and when people ask me my opinion on canon I tell them my view on canon.
Example: Carlisle and Aro are not intended by Meyer to have been anything more than friends, but we think it's there and write metas with that starting point, and have it explicitly canon in our fics.
We keep our fics consistent with one another, sometimes using a minor tidbit from canon to justifty it and sometimes making it up
Muffin and I are very stringent about this sort of thing. Our view on the characters is fixed: if something changed from one AU to another, the question is "Why?". If it just changed for no reason and the people remain the same, they're no longer real people and nothing really matters.
Example: the Volturi guards all having consistent personalities, life stories staying the same, nevermind that we made up Demetri's personality or Aro's ridiculous collection of Carlisle art.
We write metas explaining our fics on our tumblrs
See my fic meta tag. Anon asks "Why did character do thing?" and we go "well, character is a person who does things like that thing, remember in canon when they did that thing? So we had them do this thing in our fic." Nevermind that character didn't actually do thing in canon, because this was all in a fic.
Example: see the fic meta tag on my blog or Muffin's masterpost.
Now to answer your question: to my recollection Jasper/Peter and Charlotte is first mentioned in For the Love of a Woman, where Bella learns that not a single one of the Cullen men are straight and she despairs (as does Emmett, who wonders what this means for him).
It was justified as a "Jasper was in a state of ennui, they were all beautiful, they went for it" type of thing, and perhaps more to the point it tells you, the reader (and the scandalized Cullens, per fics like Bleach on the Brain) something about vampire sexual norms being different than 21st century western humans and those humans already have plenty of casual, recreational sex.
So, canon doesn't indicate it, but we had Jasper/Peter and Charlotte be a thing that happened in our fics and the argument for it can be made (I do believe sexual norms among vampires, being excempt from diseases, pregnancies, children, and the type of obligation and routine human lives have, would be... recreational).
(As it is I recall this coming up on the blog before, but I think whichever of us got the question responded with essentially the above - "We don't know, but possible".)