We describe an asymmetric approach to fMRI and MEG/EEG fusion in which fMRI data are treated as empirical priors on electromagnetic sources, such that their influence depends on the MEG/EEG data, by virtue of maximizing the model evidence. This is important if the causes of the MEG/EEG signals differ from those of the fMRI signal. Furthermore, each suprathreshold fMRI cluster is treated as a separate prior, which is important if fMRI data reflect neural activity arising at different times within the EEG/MEG data. We present methodological considerations when mapping from a 3D fMRI Statistical Parametric Map to a 2D cortical surface and thence to the covariance components used within our Parametric Empirical Bayesian framework. Our previous introduction of a canonical (inverse-normalized) cortical mesh also allows deployment of fMRI priors that live in a template space; for example, from a group analysis of different individuals. We evaluate the ensuing scheme with MEG and EEG data recorded simultaneously from 12 participants, using the same face-processing paradigm under which independent fMRI data were obtained. Because the fMRI priors become part of the generative model, we use the model evidence to compare (i) multiple versus single, (ii) valid versus invalid, (iii) binary versus continuous, and (iv) variance versus covariance fMRI priors. For these data, multiple, valid, binary, and variance fMRI priors proved best for a standard Minimum Norm inversion. Interestingly, however, inversion using Multiple Sparse Priors benefited little from additional fMRI priors, suggesting that they already provide a sufficiently flexible generative model.