Everything is possible on Tableau. If you want a blank sheet to disappear, you should hide the sheet title as well. Try using horizontal contains (one per row) and then place a vertical container one for each sheet. Now inside these vertical containers place your sheet and hide the title. This should do the trick.
However, I assume you want the titles as well - that's why I asked you to use vertical containers!! What you need to do is have these titles as separate sheets and just have the title displayed as a label for that corresponding sheet. So, you will have nine additional sheets and place then on the top of your original sheets within the vertical containers. For the title sheets, you will have to use all the filters that you've used for that corresponding sheet. Now, you finally have what you want.
Hope this helps!