The problem with stacking peltiers is that each stage needs to take not only the heat from the "load" , but also the waste heat from the peltier below. Ages ago I took apart a Sat-comms front-end that used 3 layers of peltiers to cool the front-end. From memory, the first was about 20x20mm, the second about 60x60, and the last about 200x300mm.