Hello,
One direction you could check is IF (interactive fiction). Originally these were text adventures, but there are also graphical variants of them (point and click adventures). There exist lots of authoring systems to make these programs, so you can focus on the content, and let the authoring system handle the packaging, and inter-action with the user.
I am not entirely sure it would fit your second requirement. These systems are mostly closed. You write the content, you package it, and build a program from it that you distribute to the players. They can play what you wrote, and that's it.
One way around that limit is to also give your source that you have just before "package", to the users. In principle, they can take your source, and extend or change it, if you give it a proper license (you giving permission to others to modify and re-publish the result).
That requires however that the users also have or get the authoring system that you used. For a commercial program, that's going to be problematic I think, so you might want to go with an open source authoring system instead, that runs at the major platforms (windows, mac, and perhaps linux).
Even today, communities exist that write IF, I'd say ask there too, they may have some good ideas too.
Tbh, even with an open source authoring system, I think chances are small you'll get anyone to extend. A user that extends or modifies your content would need to get and learn the authoring system, come up with a new story (which is much more work than most people are willing to spend), enter it into your story, and publish the results.
People that are capable of the above generally have so many ideas that they rather write their own stories (just like you prefer to write yours, and not extend one from someone else).
Everybody else generally doesn't get further beyond "this sucks" or "love this" or "great, keep it up", or "can you add my favorite thing X? would be cool" (even when it absolutely makes no sense at all).
You can increase the odds by making it easier for people to contribute. If you put the content at some project hosting site (github, bitbucket, etc), and you do the actual merging, repackaging, and re-distribution, would be one such step. But expect loads of feature requests :P
Other options are more radical. Instead of an IF program, make a web-site, sort of like a wiki, where each page is a small part of the story, and at the bottom you link to one or more other pages. You can make your own web-program for it. That would work even with a plain wiki program (and there are wiki hosting sites, I think, where you can just create a wiki).
I have no idea how well any of this would work.