The formation of an electric double layer composed of spherical nanoparticles is analyzed by means of a generalized Poisson-Boltzmann model and Monte Carlo simulations. We study a solution of symmetric and asymmetric mixtures of spherical particles that reside between two planar like-charged surfaces. Each spherical particle carries two elementary charges that are attached at its poles. The electrolyte solution also contains monovalent point-like salt ions. Our theoretical model properly accounts for intra-particle correlations - that is correlations between the spatially separated charges belonging to a single multivalent spherical particle. Correlations between different spherical particles are neglected. It is shown that added salt decreases the number density close to the charged surface and influences the orientation of spherical particles. Increasing salt concentration decreases the order parameter of the spherical particles. Generalized Poisson-Boltzmann results, obtained by solving an integral differential equation, and predictions from Monte Carlo (MC) simulations are in excellent agreement.