A key challenge in machine learning is to generalize from training data to an application domain of interest. This work extends the recently-proposed mixture invariant training (MixIT) algorithm to perform unsupervised learning in the multi-channel setting. We use MixIT to train a model on far-field microphone array recordings of overlapping reverberant and noisy speech from the AMI Corpus. The models are trained on both supervised and unsupervised training data, and are tested on real AMI recordings containing overlapping speech. To objectively evaluate our models, we also use a synthetic multi-channel AMI test set. Holding network architectures constant, we find that semi-supervised fine-tuning of a model pretrained on a large and diverse single-channel dataset yields the largest improvement to SI-SNR and to human listening ratings across synthetic and real datasets, outperforming supervised models trained on well-matched synthetic data. Our results demonstrate that unsupervised learning through MixIT enables model adaptation on both single-and multi-channel real-world speech recordings.