Yes, you can, i have tried. But it is wired to wear big sunglasses over my prescription eyeglasses. And others can look the eyeglasses you wear. So, it is not beautiful to wear sunglasses in such way. If you need vision aids and want to shield eyes from UV rays, you can buy prescription sunglasses, clip on sunglasses or transition sunglasses. These sunglasses can meet your vision requirements as well as give you good look. Good luck.
You'd better not do that way. I've never seen people wearing two pairs of glasses together at the same time. That would look quite strange. In addition, you will feel uncomfortable because two pairs of glasses are a little heavy and you may get pressure around your eyes. Moreover, they are easy to get scratched. There are some other choices for you if you want to prescription glasses together with sunglasses. You can either wear a pair of prescription sunglasses or clip on sunglasses which will allow you to see clearly as well protect your eyes from harmful UV rays.