A seal assembly for a turbine engine having a shaft with a rotary axis and a housing surrounding the shaft; the seal assembly being disposed between the shaft and the housing, the seal assembly comprising: an outer labyrinth seal having multiple outer fins in opposing sealing engagement with a concentric outer seal runner, one of: the outer labyrinth seal fins; and the outer seal runner, engaging the housing, and the shaft engaging an opposing one of: the outer seal runner; and the outer labyrinth seal fins; an inner labyrinth seal, disposed radially inwardly concentric to and axially overlapping the outer labyrinth seal and the outer seal runner, the inner labyrinth seal having multiple inner fins in opposing sealing engagement with a concentric inner seal runner, one of: the inner labyrinth seal fins; and the inner seal runner, engaging the housing, and the shaft engaging an opposing one of: the inner seal runner; and the inner labyrinth seal fins; and an intermediate plenum, defined between the outer fins, the inner fins, the housing and the shaft, the intermediate plenum in communication with a source of compressed gas having a supply pressure greater than an ambient pressure external to the housing and greater than an internal pressure within the housing.