Switching between multiple sliders in the same frame

I manage a dozen or so sites (and growing) that use some “standard” and some “unique” content for each of their sliders. To cut down on the time it takes to make changes that apply to all of them, I was hoping to be able to have one slider that had the standard or default content, and then a site specific one to show unique content for that particular client.

Is there any way that I could show several slides from one slider ID and then move seamlessly into another slider ID with the remaining content? I have access to all the content under a single account. Any suggestions very much appreciated!