In this paper, we present a novel multi-channel speech extraction system to simultaneously extract multiple clean individual sources from a mixture in noisy and reverberant environments. The proposed method is built on an improved multi-channel time-domain speech separation network which employs speaker embeddings to identify and extract multiple targets without label permutation ambiguity. To efficiently inform the speaker information to the extraction model, we propose a new speaker conditioning mechanism by designing an additional speaker branch for receiving external speaker embeddings. Experiments on 2-channel WHAMR! data show that the proposed system improves by 9% relative the source separation performance over a strong multi-channel baseline, and it increases the speech recognition accuracy by more than 16% relative over the same baseline.