Aerodynamic four-way coupling models are necessary to handle two-phase flows with a dispersed phase in regimes in which the particles are neither dilute enough to neglect particle interaction nor dense enough to bring the mixture to equilibrium. We include an aerodynamic particle interaction model within the framework of large eddy simulation together with Lagrangian particle tracking. The particle drag coefficients are corrected depending on relative positions of the particles accounting for the strongest drag correction per particle but disregarding many-particle interactions. The approach is applied to simulate monodisperse, rigid, and spherical particles injected into crossflow as an idealization of a spray jet in crossflow. A domain decomposition technique reduces the computational cost of the aerodynamic particle interaction model. It is shown that the average drag on such particles decreases by more than 40% in the dense particle region in the near-field of the jet due to the introduction of aerodynamic four-way coupling. The jet of monodisperse particles therefore penetrates further into the crossflow in this case. The strength of the counterrotating vortex pair (CVP) and turbulence levels in the flow then decrease. The impact of the stochastic particle description on the four-way coupling model is shown to be relatively small. If particles are also allowed to break up according to a wave breakup model, the particles become polydisperse. An ad hoc model for handling polydisperse particles under such conditions is suggested. In this idealized atomizing mixture, the effect of aerodynamic four-way coupling reverses: The aerodynamic particle interaction results in a stronger CVP and enhances turbulence levels.