Inclusions in a brush are entropically disfavored, as they constrain the surrounding brush chains and limit possible chain conformations. As a result, polymer brushes can be used in lubrication or as biological coatings against toxic molecules. Here, we study the interaction of nanoparticles with a brush using self-consistent field theory (SCFT). For a large particle compressing a brush, we reproduce the linear scaling of the repulsive potential 'Ion with the particle radius found previously using SCFT. Also, we find that this linearity gives way to a nonlinear (parabolic or cubic) dependence on the particle size for particles inserted deeply into the brush, consistent with earlier particle-based simulations. The insertion of particles disrupts the brush, changing polymer-particle interactions for subsequent nanoparticles, thus introducing effective particle-particle interactions mediated by the brush. When the grafting point is mobile in the plane of the grafting surface, our results suggest that the brush promotes clustering of inclusions. In contrast, inclusions tend to be dispersed when the grafting point is fixed. Finally, we discuss the biological implications of these findings: interactions of antimicrobial peptides with bacterial lipopolysaccharides and clustering of integrin on cancerous cell membranes.