Such a multi-stage compressor is provided that a number of valves, openings, and tubes, which are specific to two-stage compression, are arranged in an integrated manner so as to improve maintainability and compactness of the device. The compressor therefore includes a plurality of compression chambers in a housing, a medium-pressure refrigerant discharge port 123 that discharges medium-pressure refrigerant RM3 from a low-stage compression chamber of the compression chambers, a medium-pressure refrigerant suction port 122 that is open in the same direction as the medium-pressure refrigerant discharge port 123 and induces the medium-pressure refrigerant RM3 to a high-stage compression chamber of the compression chambers, a high-pressure refrigerant discharge port 124 that is open in the same direction as the medium-pressure refrigerant discharge port 123 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, and forms a medium-pressure refrigerant chamber 116 communicating with the medium-pressure refrigerant suction port 122 and the medium-pressure refrigerant discharge port 123 and having an external medium-pressure refrigerant connection induction port 126 that is open toward the outside, and forms a high-pressure refrigerant chamber 117 communicating with the high-pressure refrigerant discharge port 124 and has a high-pressure refrigerant ejection port 125 that is open toward the outside.
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