Small children can't easily handle a tall dresser for their clothing until their age reaches double digits. Chigo, a Japanese kids store, developed a stacking dresser tree for kids which gives you three two-drawer dressers that can later combine to form one six-drawer unit. It's too expensive and impractical to ship the Chigo item directly, but you can easily adapt the idea using a cheaper two-draw model.
Once you've chosen drawers you like, you'll just need to measure the height to figure out the dimensions of the side panels, cut those out of a piece of plywood, sand and paint/varnish to match your dressers, and nail or otherwise attach them to the side.
As well as being kid-friendly, this approach could also be helpful if you move a lot. When I was moving frequently in my early twenties, I tried to not buy anything too large to fit in the backseat of my car. A final bonus: if you have minimal furniture, the dressers could also serve double duty as temporary seating for a party.