<p>The goal of this article is to study a control problem for the Benney–Lin equation with multiple objectives, by means of localized interior controls. The primary objective is to steer the solution to a given control-free trajectory, along with a secondary goal of solving a non-cooperative/competitive optimization problem associated with the solution of underlying control system. To study such multi-objective hierarchical control problem, we employ a well-known Stackelberg–Nash strategy. More precisely, assuming the existence of a control (referred to as <i>leader</i>) responsible for driving the solution to a free trajectory, we characterize the other two controls (referred to as <i>followers</i>) which solve the non-cooperative optimization problem under study. The characterization of the followers is influenced by the choice of leader, leading to a coupled optimality system. Consequently, this multi-objective control problem for the Benney–Lin equation simplifies to a single-objective control problem for the optimality system.</p>