High bleed flow muffling systems are disclosed. Example muffling devices according to at least some aspects of the present disclosure may include a first orifice plate and a second orifice plate at least partially defining a plenum arranged to receive the flow of a compressible fluid. The first orifice plate and the second orifice plate may be arranged to produce cross-impinging flow such that flow through the orifices of the first orifice plate into the plenum is directed at the wall of the second orifice plate and such that flow through the orifices of the second orifice plate is directed at the wall of the first orifice plate. Some example embodiments may include an inlet flow restrictor disposed upstream of the first and second orifice plates.