Is there an issue with splitting up papers already posted on ArXiV? A co-author and I completed a paper and posted it on ArXiV. Since then, the paper has been rejected many times. The paper has a few good ideas in it, but they were not put in context nor executed well. We have decided it is not worth submitting in its current form, and my co-author has repeatedly made clear they do not want to work on the paper any longer.
However, I would like to re-do the paper nearly from scratch and take it in a totally different direction that I believe is much more interesting. The parts of the paper I am interesting in bringing to the new paper are parts I did alone in the original paper, and my co-author agrees they did not contribute to these parts. But if the old paper remains on ArXiV as a separate paper, the new paper will have too many similarities.
So my question is: In this situation, could I replace the old arxiv paper with the new one and remove my co-author as an author (they are fine with this)? Is this something that people would find strange? It will be clear that the papers are very different.
No, you shouldn't replace the old paper with the new one.  Replacements are supposed to be revisions, not &quot;very different&quot; papers.  The replacement that you propose would not only revise your contributions; it also looks like an attempt to erase your coauthors' contributions.  The change in authors would almost certainly raise a red flag with the moderators (through arXiv's auto-moderation software), and I expect most moderators would reject the replacement.
Submitting a new paper whose text significantly overlaps an existing arXiv preprint will also raise a red flag with the moderators, but as Dan Ramras suggests in a comment, explicitly acknowledging the overlap will convince most moderators to accept it anyway.
(I was an arXiv moderator for over a decade.)