Is there a minimum amount of methodological modifications for extending previous work from other authors? Given a published paper, as a Computer Scientist, I see an opportunity to extend the work and methodology of previous authors. 

By modifying the presented work, introducing some concepts and a different approach for input parameters (for example) my "new" work can achieve better results than the results presented by the original authors.

In some cases, the modifications I suggest are not extensive or radically divergent, but even this way the results are better than the current state of the art.

Is there considered to be a minimum change from the methodology in the original paper, to publish an extension of that earlier paper from other authors? 

EDIT: By extending I mean: writing a paper emphasizing the modifications that produce improved/better results, instead of copying significant passages from the original work results.
You need a little bit more than for the results to be better than the state of the art - you need the modification to be a non-obvious one that moves the field forward.

For example, there are a lot of results in my field that I can improve by tuning some parameters (to make the results in a given scenario "better") or by combining two known methods. If the modification involves new intellectual or technical insight, it's a meaningful extension and can be published. Otherwise, it's probably not publishable. 

The "minimum" modification that is necessary for the work to be publishable is the modification that involves (at least) the amount of new intellectual content that is necessary for work in your field to be considered publishable.