As far as I know, there is no "Easy Button" in Tableau for this.
You can either:
build a separate view/dashboard for each iteration you need to be able to print and then just print the full workbook (tedious)
utilize tabcmd command line utility tool (assuming you have Tableau Server since you're talking about download PDF) and build a .bat file to issue the commands to "change the filter and print to PDF" for each dimension member desired. (complicated)
You could get super fancy and build your .bat instructions dynamically from a query somehow. I am out of my depth at this point, but I know it's possible. (even more complicated)
Sorry--hope this is at least helpful.
Thanks for your reply.