I have dealt with this situation before. My solution was to use a calculated field:
with the compute using set and combined with the correct data structure and worksheet setup, you can have exact control over multiple marks.
If you can upload a sample workbook, an example can be made for you, also you can watch my 5 min tips and tricks video from the customer conference at the bottom of the page at http://www.tableausoftware.com/tcc11-sessions
Hi Joe, thanks for the reply. I watched the video, and I think I understand the general principle, but half-way through the steps the process broke down because in my case, "compute using" doesn't provide the advanced/custom option for some reason. Admittedly, I have the data sources coming from separate sources, rather than a merged single table as you recommend in the video, may be this is the problem.
I've uploaded a reduced version of the workbook I'm working with here:
One of the user parameters ("Participation metrics") has an option "none". The goal is to have the pie chart layer disappear when this is selected, leaving only the polygons.