The present paper is a sequel to the paper by Karchev (2008 J. Phys.: Condens. Matter 20 325219). A two-sublattice ferrimagnet, with spin- s(1) operators S(1i) at the sublattice A site and spin-s(2) operators S(2i) at the sublattice B site, is considered. Renormalized spin-wave theory, which accounts for the magnon-magnon interaction, and its extension are developed to describe the two ferrimagnetic phases (0,T(*)) and (T(*),T(N)) in the system, and to calculate the magnetization as a function of temperature. The influence of the parameters in the theory on the characteristic temperatures T(N) and T(*) is studied. It is shown that, increasing the inter-sublattice exchange interaction, the ratio T(N)/T(*)>1 decreases approaching one, and above some critical value of the exchange constant there is only one phase T(N) = T(*), and the magnetization-temperature curve has the typical Curie-Weiss profile. When the intra-exchange constant of the sublattice with stronger intra-exchange interaction increases the Néel temperature increases while T(*) remains unchanged. Finally, when the magnetic order of the sublattice with smaller magnetic order decreases, T(*) decreases. The theoretical predictions are utilized to interpret the experimentally measured magnetization-temperature curves.