We have studied CR of nanoparticles in the presence of electrolyte containing multivalent ions. Differently from the earlier approaches which studied CR for a semi-grand canonical system , in which suspension is separated from the reservoir by a semipermeable membrane, the present theory is constructed directly for an isolated suspension (canonical ensemble) . It is important to stress that for a semi-grand canonical system, presence of Donnan potential between system and its implicit reservoir results in titration isotherms (plotted as a function of reservoir pH) that can be very different from those of an isolated system . Furthermore, we stress that the usual constant pH simulation methods allow us to control only the pH of the reservoir and not the pH of the system 107 . The theory presented in this paper applies directly to isolated suspensions, without invoking an external reservoir. The comparison with simulations shows that the theory is very accurate for suspensions containing 1:z electrolytes at all pH values. The theory is also able to accurately predict ionic depletion close to hard walls -this depletion is driven by the electrostatic correlations between cations and anions of electrolyte. Taking advantage of the good accuracy of the theory for predicting the ionic density profiles, we have used the well-known contact value theorem to calculate the osmotic pressure of suspensions of nanoparticles for different pH values and salt concentrations. We have also shown that if suspension contains multivalent counterions, the present theory looses its accuracy. This is a consequence of strong electrostatic correlations between the multivalent cations and the adsorbed protons, which cannot be accounted for in the framework of the present theory. This will be the subject of the future work.