This paper proposes a method to estimate spillover effects of a random treatment using a nonrandom sample of individuals for whom the analyst can observe their outcomes, i.e., nonrandom sample selection. Although randomized experiments facilitate comparisons between treated and control groups at the baseline, they cannot guarantee that the groups are comparable when there is endogenous sample selection. The proposed method employs an exposure monotonicity assumption that extends the conventional Lee bounds to multiple treatments. Under this assumption, I show how to compute the bounds for a spillover estimand that allows for the inclusion of covariate adjustments and network dependence, where statistical inference follows a design-based approach. In my empirical application, I apply the new method to analyze an anticonflict intervention on student behavior and find negative spillover effects on classroom misconduct episodes.