Publishing an incomplete idea
Also, the first piece is actually of limited technical use but introduces the concepts, notations, and methods required for the further pieces.


The main question is whether this work is of independent interest or use to anybody but you.  All research is incomplete in some sense, and that doesn't bother people (everyone likes opportunities for further work).  So the issue is whether your paper is incomplete in the sense of not accomplishing anything interesting yet, or incomplete in the sense that there is still much more to do.

If there are people who want to read it now, on its own, then that's an argument for publishing it now.  If it has little value except as preparation for the next paper, and that paper is already written, then it might be OK, but getting it accepted on its own may be tough.  If it has little value except as preparation for a future paper that does not yet exist and might not pan out, then it will be really difficult to publish it.