Gah!

So I have a Paragard IUD and my periods are super heavy for about two or three days. I've been dealing with it by using my DivaCup with a heavy day cloth pad as backup. These usually get me through, but today I was totally amazed....I overflowed my size 2 DivaCup three times in five hours....AT WORK! 

I hate changing my cup at my job, because it's at a school with bathroom stalls. It's not a sanitary or conducive to emptying and rinsing my cup. I get blood all over my hand, and it's gross. I had to take a wad of paper towels with me every time I had to change my cup, and I still had to be stealthy when exiting the stall so as not to disgust anyone with my blood-stained hand. GRR!

So! My question is this: is there a cup that holds even more than the size 2 DivaCup? I looked at the brand comparison charts and tags already, and I see that there is some debate over how much the cups actually hold...so I'm wondering if anybody here has had a size 2 DivaCup and found another cup that holds even more. In one of the comments, I saw that the Mia Cup apparently holds 30mL...is that correct?

Anyway, any help you ladies can give me would be greatly appreciated. I definitely want to find some way to remedy this issue.