In this talk, I present results on a stationary mean-field model with singular controls for a Markov modulated Itô-diffusion, in which the representative agent interacts with a long-time conditional weighted average of the population through a discounted performance criterion. Natural applications are in the context of irreversible production expansion in dynamic oligopolies, where the dynamics of the production capacity is affected by the market's business cycles and the price of the produced good depends on the aggregate stationary production of the whole industry. We prove existence and uniqueness of the mean-field stationary equilibrium and we characterize it through a system of nonlinear equations. Along the way, explicit results for the joint stationary distribution of the controlled production capacity and the Markov chain at equilibrium are also derived. A numerical analysis allows to understand properties of the mean-field equilibrium.