Combining end-to-end neural speaker diarization (EEND) with vector clustering (VC), known as EEND-VC, has gained interest for leveraging the strengths of both methods. EEND-VC estimates activities and speaker embeddings for all speakers within an audio chunk and uses VC to associate these activities with speaker identities across different chunks. EEND-VC generates thus multiple streams of embeddings, one for each speaker in a chunk. We can cluster these embeddings using constrained agglomerative hierarchical clustering (cAHC), ensuring embeddings from the same chunk belong to different clusters. This paper introduces an alternative clustering approach, a multi-stream extension of the successful Bayesian HMM clustering of x-vectors (VBx), called MS-VBx. Experiments on three datasets demonstrate that MS-VBx outperforms cAHC in diarization and speaker counting performance.