The Animatrix seems like a real example of something along those lines. A DVD of 6 short episodes that expanded on the Matrix story universe. They were done by different directors/writers/makers, like authorised fanfic or something. In my opinion it was a great addition, better than the full-blown sequels, and certainly not a distasteful cash-grab.

I think this could totally work for something like Inception too. The film has a backstory suggests at a wider context beyond what's shown in the scenes. Most stories do. That's why fanfiction exists.