We study multi-stream transmission in the $K \times N \times K$ channel with interfering relay nodes, consisting of $K$ multi-antenna source--destination (S--D) pairs and $N$ single-antenna half-duplex relay nodes between the S--D pairs. We propose a new achievable scheme operating with partial effective channel gain, termed multi-stream opportunistic network decoupling (MS-OND), which achieves the optimal degrees of freedom (DoF) under a certain relay scaling law. Our protocol is built upon the conventional OND that leads to virtual full-duplex mode with one data stream transmission per S--D pair, generalizing the idea of OND to multi-stream scenarios by leveraging relay selection and interference management. Specifically, two subsets of relay nodes are opportunistically selected using alternate relaying in terms of producing or receiving the minimum total interference level. For interference management, each source node sends $S \,(1 \le S \le M)$ data streams to selected relay nodes with random beamforming for the first hop, while each destination node receives its desired $S$ streams from the selected relay nodes via opportunistic interference alignment for the second hop, where $M$ is the number of antennas at each source or destination node. Our analytical results are validated by numerical evaluation.