We consider bilevel programs where a single leader interacts with multiple followers who are coupled by a Nash equilibrium problem at the lower level. We generalize the value function reformulation to include multiple followers. This allows us to propose a convergent method based on the sequential convex approximation paradigm, and study the (exact or inexact) iterative solution of the convex subproblems. Since some of our convergence results require a constraint qualification, we give conditions under which it is satisfied. Finally, we propose a novel ESG-oriented multi-portfolio selection model, and test our numerical procedure confirming the theoretical insights.