The estimation of spillover and peer effects presents challenges that are still unsolved. In particular, even if in samples of networks separate algebraic identification of endogenous and exogenous effects is possible (Bramoullé et al., 2009), these might be contaminated by the simultaneous dependence of outcomes and covariates upon unobserved factors (Angrist, 2014). In this paper we expand the standard framework for the analysis of peer effects and social interactions, to allow for a complex structure of unobsorved "common shocks" (contextual effects) in a network. These common shocks correlate across nodes with both outcomes and covariates, introducing a source of endogeneity in the model. We allow for both a "group" and a "network" structure of common shocks, to which we attach a different socio-economic interpretation in the context of peer effects at school. We outline conditions under which identification of all parameters of interest is possible in terms of data generation process and network structure. In particular, "endogenous" and "exogenous" social effects are separately identified so long as the "group" and the "network" structure of the unobservables are not fully overlapping. This allows to establish appropriate first and second moment conditions which are well suited for GMM estimation. In Monte Carlo simulations, we compare our proposed methodology to others that are more established in the literature but do not allow for this more general instance of simultaneity.