What to do when you have more things to say in a published paper? I have published a paper covering a topic, now I see that there is a lot more to say about the published work, mainly in the theoretical framework and in the results/conclusion sections. However, I don't see how these information can merit their own paper.

How can I publish these additional information since the main core the work has been already published?

The best I came up with is to talk about these additional information in a conference paper, is that possible? Can I maintain the same results from the original paper ? what do you suggest?
Writing a paper that extends another is pretty common practice. It could be published anywhere that will accept it. 

But if the results in the new paper are insufficiently novel then it might be hard to find a venue that accepts it. If the conclusions of the new paper are obvious to readers of the old one, reviewers will probably notice it and editors won't be very inclined to want to publish it. 

The theoretical underpinnings may be a different matter. They may stand on their own as a separate paper. Or not. But reviewers and editors will judge that also.