A cooling arrangement for a gas turbine engine according to an example of the present disclosure includes, among other things, an offtake duct that has an offtake inlet coupled to a cooling source, the offtake duct defining a throat, and a valve downstream of the throat. The valve couples the offtake duct and a first cooling flow path. The valve is operable to selectively modulate flow through the offtake duct. A bleed passage includes a bleed inlet coupling the offtake duct and a second cooling flow path. The bleed inlet is defined at a location between the offtake inlet and the throat, inclusive.