A first cooling stage is fluidly coupled to a bleed port of a compressor to receive and cool bleed air with the air stream to produce a cool bleed air. A cooling pump receives and increases a pressure of the cool bleed air to produce a pressurized cool bleed air. A second cooling stage is fluidly coupled to the pump to receive and cool the pressurized cool bleed air to produce an intercooled cooling air. A valve is downstream of the first cooling stage, the valve selectively delivering air into a mixing chamber where it is mixed with air from a tap that is compressed to a higher pressure than the air from the bleed port, and the valve also selectively supplying air from the first cooling stage to a use on an aircraft associated with the gas turbine engine. A method is also disclosed.