In this paper, a composed A + B magnetic system, with spins JA = 2 and JB = 3/2, is considered within the mean-field approximation, in the framework of Tsallis nonextensive statistics. Our motivation is twofold: (1) to approach the existing experimental data of manganese oxides (manganites), where Mn3+ and Mn4+ form two magnetic sublattices, and (2) to investigate the structure of nonextensive density matrices of composed systems. By imposing that thermodynamic quantities, such as the magnetization of sublattices A and B, must be invariant whether the calculation is taken over the total Hilbert space or over partial subspaces, we found that the expression for the nonextensive entropy must be adapted. Our argument is supported by the calculation of sublattice magnetizations MA and MB, internal energy, UA and UB and magnetic specific heat, CA and CB. It is shown that only with the modified entropy, the two methods of calculation agree to each other. Internal energy and magnetization are additive, but no clear relationship was found between SA, SB and the total entropy SA+B for q ≠ 1. It is shown that the reason for the failure of the standard way of calculation is the assumption of statistical independence between the two subsystems, which however does not affect the density matrix in the full Hilbert space.