A conditioned air delivery system is provided for parked aircraft. The system can accommodate elevated thermal loads while maintaining operation, albeit with reduced flow rates or slightly elevated temperatures. When temperature set points are not reached or cannot be maintained, a second compressor of a refrigeration unit is operated in parallel with a first compressor. When refrigerant pressure becomes excessive, a second fan is operated that is associated with a condenser of the system. Still higher pressures, indicative of higher thermal loads, can cause the system to shut down operation of one of the compressors, reducing the overall cooling capacity of the system, while maintaining the supply of refrigerated air to the aircraft. The airflow may be reduced to maintain an air temperature at or near the desired temperature. Coordination of several parallel and redundant refrigeration units may be provided with a single blower and coordinated control.