Delayed Republish – no interruption

How do I delay the republishing of a post (with new content) without interrupting the current post?

I went in and tried to just reschedule the post to release in a couple of days, but it took the current post down…

Background: I post a weekly economic update (hyperlinked PDF) and I like to just ‘open’ the new link every Monday morning. I generally get the new content the Friday/Saturday before, so I would love to upload the new pdf, make the changes to the link, and schedule those to happen without interrupting the current list of economic update pdfs, hope that makes sense. Thanks for your suggestions.