Machine learning models are often implemented in cohort with humans in the pipeline, with the model having an option to defer to a domain expert in cases where it has low confidence in its inference. Our goal is to design mechanisms for ensuring accuracy and fairness in such prediction systems that combine machine learning model inferences and domain expert predictions. Prior work on "deferral systems" in classification settings has focused on the setting of a pipeline with a single expert and aimed to accommodate the inaccuracies and biases of this expert to simultaneously learn an inference model and a deferral system. Our work extends this framework to settings where multiple experts are available, with each expert having their own domain of expertise and biases. We propose a framework that simultaneously learns a classifier and a deferral system, with the deferral system choosing to defer to one or more human experts in cases of input where the classifier has low confidence. We test our framework on a synthetic dataset and a content moderation dataset with biased synthetic experts, and show that it significantly improves the accuracy and fairness of the final predictions, compared to the baselines. We also collect crowdsourced labels for the content moderation task to construct a real-world dataset for the evaluation of hybrid machine-human frameworks and show that our proposed learning framework outperforms baselines on this real-world dataset as well.