Cross-modal enhancement (CME) occurs when the neural response to a stimulus of one modality is augmented by another stimulus of a different modality. Paired stimuli of the same modality never produce supra-additive enhancement but may produce modality-specific suppression (MSS), in which the response to a stimulus of one modality is diminished by another stimulus of the same modality. Both CME and MSS have been described for neurons in the deep layers of the superior colliculus (DSC), but their neural mechanisms remain unknown. Previous investigators have suggested that CME involves a multiplicative amplifier, perhaps mediated by N-methyl D-aspartate (NMDA) receptors, which is engaged by cross-modal but not modality-specific input. We previously postulated that DSC neurons use multisensory input to compute the posterior probability of a target using Bayes' rule. The Bayes' rule model reproduces the major features of CME. Here we use simple neural implementations of our model to simulate both CME and MSS and to argue that multiplicative processes are not needed for CME, but may be needed to represent input variance and covariance. Producing CME requires only weighted summation of inputs and the threshold and saturation properties of simple models of biological neurons. Multiplicative nodes allow accurate computation of posterior target probabilities when the spontaneous and driven inputs have unequal variances and covariances. Neural implementations of the Bayes' rule model account better than the multiplicative amplifier hypothesis for the effects of pharmacological blockade of NMDA receptors on the multisensory responses of DSC neurons. The neural implementations also account for MSS, given only the added hypothesis that input channels of the same modality have more spontaneous covariance than those of different modalities.