An apparatus and method for compressing gas refrigerant using two different compressors operated alternatively in a series or parallel mode for obtaining two different compression ratios and thereby provide efficient operation for both a relatively lower suction pressure and a relatively higher suction pressure. This system avoids an unbalanced mass flow rate when the compressors are operated in series by unloading a downstream one of the compressors. When operated in the series mode, refrigerant is bypassed back to a suction inlet of the downstream compressor during a portion of a compression stroke of the downstream compressor for equalizing the mass flow rate through the two compressors.