In this paper, we investigate the regimes of velocity accommodation and of load transmission within a dry sliding interface, in the presence of a solid and discontinuous interfacial layer (the so-called third body). To that end, an appropriate numerical framework called the multibody meshfree approach is used to implement a local model of such an interface, and a comprehensive dimensionless parametric study is performed in order to analyse the influence of the mechanical properties of the third body on the interfacial solid flow regimes, on the friction coefficient, and on the modes of energy dissipation. To that end, the concept of partial coefficient of friction is introduced. The numerical results demonstrate that the friction in the interface is limited by changes in the kinematics of the shear accommodation in the third-body layer and by the activation of different modes of energy dissipation (related either to surface area creation/destruction in the third-body layer or to bulk deformation of the solid matter composing it) which are uncorrelated in the parametric space of the mechanical properties of the third-body particles.