Menstrual cup with an IUD?

I recently transitioned from hormonal BC (the pill) to the non hormonal copper IUD. I loved the pill but was on it for 3 years and wasn’t crazy about the hormones. On the pill, I didn’t have a full period for over 2 years. Now that I’m getting periods again, I’m trying to find the period products I like best.

Has anyone with an IUD tried a menstrual cup or disc? Have you had problems with it, did it affect your IUD in any way?

I’d love any advice/tips/stories!