Combined Use of Menstrual Cup and Sponge

I recently started to use a menstrual cup, and I am loving the freedom. However, it still doesn't keep things leak free, especially since I have a very heavy flow (and it isn't a case of improper insertion/use). I heard about menstrual sponges, and was wondering if anyone has experience with using both methods in combination with each other. I want to stop relying on pads/liners, and want to compare this method to purchasing period panties.
Thanks!