  In this paper a composed A+B magnetic system, with spins J_A=2 and J_B=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 Mn^{3+} and
Mn^{4+} 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 weather 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 calculation of
sublattices magnetization M_A and M_B, internal energy, U_A and U_B, 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 S_A,
S_B and the total entropy S_{A+B} for q \neq 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.
