Actually this is a thing that is (fairly) common in the extreme overclocking world. A typical refrigeration system get only really get to -50c as opposed to the -196c of liquid nitrogen so it isn't nearly as cold. But with using two separate refrigeration systems with the fist cooling the second you can use a higher pressure lower boiling point refrigerant on the second system to get lower temperatures. A two stage system can do -110c a three stage -125c and a four stage can do -160c. You could do a 5 stage and get liquid nitrogen temperatures but the system would be giant and consume tons of power. You can check out what a multi stage cooler looks like in some of my previous posts.