Adding additional magnet to mag safe case for iphone 13

I have a new iPhone 13 mini and purchased the apple magsafe case. Without the case, my iPhone sits securely against my existing magnetic vent mount. With the case, the phone no longer sits securely and in fact falls off when driving on a curve or bumpy road. I was thinking of adding an additional magnet sticker to the inside of the mag safe case (as I did with my previous iPhone 8). Two questions: 1. Could I damage the phone by adding an additional magnet to the mag safe case? 2. Does anyone know of an additional magnet which can be added that will also allow for securing the phone to a mag safe vent mount car charger?