Leveraging cross-species information in protein function prediction can add significant power to network-based protein function prediction methods, because so much functional information is conserved across at least close scales of evolution. We introduce MUNDO, a new cross-species co-embedding method that combines a single-network embedding method with a co-embedding method to predict functional annotations in a target species, leveraging also functional annotations in a model species network.;Across a wide range of parameter choices, MUNDO performs best at predicting annotations in the mouse network, when trained on mouse and human protein-protein interaction (PPI) networks, in the human network, when trained on human and mouse PPIs, and in Baker's yeast, when trained on Fission and Baker's yeast, as compared to competitor methods. MUNDO also outperforms all the cross-species methods when predicting in Fission yeast when trained on Fission and Baker's yeast; however, in this single case, discarding the information from the other species and using annotations from the Fission yeast network alone usually performs best.;All code is available and can be accessed here: github.com/v0rtex20k/MUNDO.;Supplementary data are available at Bioinformatics Advances online. Additional experimental results are on our github site.