An intercooled cooling system for a gas turbine engine includes a heat exchanger in fluid communication with a cooling airflow source directed through the heat exchanger and an auxiliary compressor fluidly coupled to the heat exchanger via a discharge duct to compress the cooling airflow exiting the heat exchanger. A compressor discharge pathway directs a first portion of the cooling airflow from the auxiliary compressor to a first cooling location of the gas turbine engine, and a bypass pathway is fluidly coupled to the discharge duct between the heat exchanger and the auxiliary compressor to direct a second portion of the cooling airflow to a second cooling location of the gas turbine without passing through the auxiliary compressor.