Is there a minimum amount of methodological modifications for extending previous work from other authors?
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.