A cascading selective microwave directional amplifier (cascade) includes a set of Josephson devices, each Josephson device in the set having a corresponding operating bandwidth of microwave frequencies. Different operating bandwidths have different corresponding center frequencies. A series coupling is formed between first Josephson device from the set and an nth Josephson device from the set. The series coupling causes the first Josephson device to amplify a signal of a first frequency from a frequency multiplexed microwave signal (multiplexed signal) in a first signal flow direction through the series coupling and the nth Josephson device to amplify a signal of an nth frequency in a second signal flow direction through the series, where the second signal flow direction is opposite of the first signal flow direction.