Multicast ATM switch is in great demand for the future communication network. We have proposed the Batcher banyan network with cell copy preparation stages as a transit switch. It performs cell replication with small hardware increase. On the trunkline, multicast traffic is quite little, thus hardware for cell copy can be sustained small. In those previous works, the effect of the external blocking was omitted. In this paper, we propose a multicast switching network which adopts the incomplete copy network that we have proposed, and examine several strategies to prevent the external blocking for this switching network. Namely, the input buffer method with an arbitration network is applied. For multicast usage, we propose two modifications. One is to arbitrate after cell replication for the sake of simple control and small hardware. The other is to annex a cell distribution network for smoothing biased cell arrival. Biased cell arrival occurs because the output of the incomplete copy network is not uniform. Simulation results show the effectiveness of the proposed method.