What to do when you have more things to say in a published paper?
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.