In this paper, we describe a method to tackle data sparsity and create recommendations in domains with limited knowledge about user preferences. We expand the variational autoencoder collaborative filtering from a single-domain to a multi-domain setting. The intuition is that user-item interactions in a source domain can augment the recommendation quality in a target domain. The intuition can be taken to its extreme, where, in a cross-domain setup, the user history in a source domain is enough to generate high-quality recommendations in a target one. We thus create a Product-of-Experts (POE) architecture for recommendations that jointly models user-item interactions across multiple domains. The method is resilient to missing data for one or more of the domains, which is a situation often found in real life. We present results on two widely-used datasets - Amazon and Yelp, which support the claim that holistic user preference knowledge leads to better recommendations. Surprisingly, we find that in some cases, a POE recommender that does not access the target domain user representation can surpass a strong VAE recommender baseline trained on the target domain.