<p>Thermoelectric coolers (TEC) play a critical role in establishing substantial temperature differences required for cooling photoelectric detectors. While single-stage devices suffice for moderate cooling, multi-stage TECs are indispensable when pursuing cryogenic cooling below 200 K. The existing multi-stage TECs, however, remain constrained by their exclusive dependence on Bi<sub>2</sub>Te<sub>3</sub>-based alloys. Recently, the n-type Mg<sub>3</sub>Bi<sub>2</sub>-based material with high thermoelectric performance around room temperature has been discovered. Herein, we report the design of the double-stage TEC with 7 pairs of thermoelectric legs in the upper stage and 17 pairs of legs in the bottom stage, utilizing the n-type Mg<sub>3.1</sub>Sb<sub>0.497</sub>Bi<sub>1.5</sub>Te<sub>0.003</sub> in combination with p-type (Bi, Sb)<sub>2</sub>Te<sub>3</sub>. An assembly process that enables precise integration of thermoelectric legs with ceramic substrates through a one-step reflow soldering has been developed. When operating at a hot-side temperature of 350 K, the double-stage TEC achieves a maximum cooling temperature difference of ~103.2 K. The cooling performance of this double-stage TEC is comparable to that of the device based on commercial Bi<sub>2</sub>Te<sub>3</sub> alloys. Our results demonstrate that n-type Mg<sub>3</sub>Bi<sub>2</sub>-based materials are highly promising for thermoelectric cooling applications.</p>