A lower pressure tap is connected to a first heat exchanger to be cooled by cooling air, and then to a selection valve. The selection valve selectively delivers the lower pressure tap air to a boost compressor. The lower pressure tap air downstream of the boost compressor is connected to cool the at least one turbine. The selection valve also selectively delivers a portion of the lower pressure tap air across a first cooling turbine, and to a line associated with an air delivery system for a cabin on an associated aircraft. A portion of the air downstream of the first cooling turbine is connected to a second cooling turbine, and air downstream of the second cooling turbine is connected for use in a cold loop A method of operating an air supply system is also disclosed.