We study the formation of multilayer networks where payoffs are determined by the de- grees of players in each network. We begin by imposing either concavity or convexity in degree on the payoff function of the players. We then explore distinct network relationships that result from inter- and intra-network spillovers captured by the properties of supermod- ularity/submodularity and strategic complementarity respectively. We show the existence of equilibria and characterize them. Additionally, we establish both necessary and sufficient con- ditions for an equilibrium to occur. We also highlight the connection, in equilibrium, between inter-network externalities and the identity of linked players in one network given the identity of linked players in the other network. Furthermore, we analyze efficient multilayer networks. Finally, we extend our models to contexts with more than two layers, and scenarios where agents receive a bonus for being connected to the same individuals in both networks.