This paper proposes a new method to identify and estimate the parameters of an extension of a linear model of peer effects where individuals form different types of social and professional connections that can affect their outcomes. A stylized model provides a theoretical framework for the peer effects linear specification and the main identifying assumptions, which are used to provide identification results in a setting that allows all layers in the multilayer network to be endogenous. I show that identifying heterogeneous network effects is possible under the assumption that the dependence between individuals in the population is characterized by a stochastic process where dependence vanishes in the network space. I offer a novel multilayer measure of distance that provides a source of exogenous variation used to form identifying moment conditions. I propose a Generalized Method of Moments estimator that is consistent and asymptotically normal at the standard rate, for which I characterize the asymptotic variance-covariance matrix that considers the intrinsic network dependence among individuals. A Monte Carlo experiment confirms the desirable finite properties of the proposed estimator, and an empirical application finds positive and significant peer effects in citations from a multilayer network of professional connections.