A compressor system includes a first compressor assembly including at least one first impeller. The first compressor assembly defines at least one first volute configured to receive a first working fluid from the at least one first impeller at a first pressure and a first temperature. The compressor system also includes a second compressor assembly rotatably coupled to the first compressor assembly. The second compressor assembly includes at least one second impeller rotatably coupled to the at least one first impeller. The second compressor assembly defines at least one second volute configured to receive a second working fluid from the at least one second impeller at a second pressure. Further, at least one of the following conditions exist, i.e., the first pressure is different from the second pressure and the first temperature is different from the second temperature.