A multi-stage compressor , comprising: a plurality of compression chambers formed in a housing ; a medium-pressure refrigerant discharge port that discharges medium-pressure refrigerant from a low-stage compression chamber of the compression chambers ; a medium-pressure refrigerant suction port that is open in a same direction as the medium-pressure refrigerant discharge port and induces the medium-pressure refrigerant into a high-stage compression chamber of the compression chambers ; a high-pressure refrigerant discharge port that is open in a same direction as the medium-pressure refrigerant discharge port and discharges high-pressure refrigerant discharged from the high-stage compression chamber of the compression chambers ; and a refrigerant connection cover that is detachably mounted on the housing , wherein the refrigerant connection cover forms a medium-pressure refrigerant chamber , which communicates with the medium-pressure refrigerant suction port and the medium-pressure refrigerant discharge port and which has an external medium-pressure refrigerant connection induction port that is open toward an outside, wherein the refrigerant connection cover forms a high-pressure refrigerant chamber , which communicates with the high-pressure refrigerant discharge port and which has a high-pressure refrigerant ejection port open toward an outside, wherein the multi-stage compressor is a scroll compressor including an orbiting scroll and a fixed scroll , and the fixed scroll constitutes a part of the housing , and the refrigerant connection cover is mounted on the fixed scroll , wherein the medium-pressure refrigerant chamber includes a recess portion of the fixed scroll and a recess portion of the refrigerant connection cover that are facing each other, wherein the high-pressure refrigerant chamber includes a recess portion of the fixed scroll and a recess portion of the refrigerant connection cover that are facing each other. a plurality of compression chambers formed in a housing ; a medium-pressure refrigerant discharge port that discharges medium-pressure refrigerant from a low-stage compression chamber of the compression chambers ; a medium-pressure refrigerant suction port that is open in a same direction as the medium-pressure refrigerant discharge port and induces the medium-pressure refrigerant into a high-stage compression chamber of the compression chambers ; a high-pressure refrigerant discharge port that is open in a same direction as the medium-pressure refrigerant discharge port and discharges high-pressure refrigerant discharged from the high-stage compression chamber of the compression chambers ; and a refrigerant connection cover that is detachably mounted on the housing , wherein the refrigerant connection cover forms a medium-pressure refrigerant chamber , which communicates with the medium-pressure refrigerant suction port and the medium-pressure refrigerant discharge port and which has an external medium-pressure refrigerant connection induction port that is open toward an outside, wherein the refrigerant connection cover forms a high-pressure refrigerant chamber , which communicates with the high-pressure refrigerant discharge port and which has a high-pressure refrigerant ejection port open toward an outside, wherein the multi-stage compressor is a scroll compressor including an orbiting scroll and a fixed scroll , and the fixed scroll constitutes a part of the housing , and the refrigerant connection cover is mounted on the fixed scroll , wherein the medium-pressure refrigerant chamber includes a recess portion of the fixed scroll and a recess portion of the refrigerant connection cover that are facing each other, wherein the high-pressure refrigerant chamber includes a recess portion of the fixed scroll and a recess portion of the refrigerant connection cover that are facing each other. <EOS>