I'm planning to decorate a shoe box and I was hoping to strengthen the cardboard if possible first. It's already pretty sturdy but I was just wondering if there were any ways to "stiffen" it any better first.

Maybe you could incorporate some kind of strengthening wire into the box (in each corner and edge and side) and then cover it with a lining inside the box?

You could paper mache over it?

glue a layer of museum board around it (or inside of it).