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Social network analysis is a growing and popular field in statistics sincethe second half of the last century. Although single networks have been largely studiedand a variety of models has been developed for their analysis, multidimensionalnetworks are still a young and quite unexplored subject. In most cases, the attentionhas been focused on the specific case of dynamic networks. The aim of the presentwork is to provide with an extension of latent space models for network analysisto the case of multidimensional networks. We also introduce node-specific effects(sender and receiver effects), typical to the single network literature, to allow for amore flexible representation of the multidimensional network. Finally, a real dataapplication will be presented.