I contributed to a paper to a journal in the life sciences. The paper contains a lot of field-specific theory, but the main point relies on a result obtained through some new inference method that I worked out. Since the method was not the focus of the paper, I described it in a terse, but pretty general, supplement to the paper. The code implementation was not included.
We think this method and its implementation are of a general interest to the community, and would like to submit a separate second paper which will expand on the supplement, and provide new sample applications. In principle, there would be a lot of overlap: identical text in the derivations, similar notes, etc. Is this plagiarism? And generally, at what point would it cease being plagiarism? Obviously tacking on an introduction and a conclusion would not be okay (or would it?), but what about past that?
A related question is this: New paper which is very similar, but subtly different, from previous paper. However, the difference in my situation is that I won't be making any big additional theoretical contributions.