Fan continuations?

I've been re-reading a lot of my favorite stories here. Most of them, sadly, are cancelled and will never be completed.

When a story you love ends prematurely, you can't help but think up your own interpretation of how it would be continued and ended. These ideas may be enough to be written down and, with consent from the author, shared.

I've actually written an outline of how I'd conclude my favorite story. I've been tempted to finish it and perhaps write some other continuations for other stories I like. However, I've been torn between doing that, or simply creating works of my own that simply share similar themes, but are fanworks of my own hand.

What do you think?