Herein, thermomagnetic properties of a ferro‐ferrimagnetic system with magnetic moments of values , and alternating on a square lattice, are investigated. These properties are framed in hysteresis, double‐spin compensation, and discontinuous behavior of the system. Through Monte Carlo simulations, the temperature dependence of the magnetization and magnetic susceptibility of the system for zero and nonzero values of an applied external magnetic field are analyzed. The hysteresis behavior of the model for different temperature values is also studied. It is found that the system experiences double‐spin compensation and multiple hysteresis loops when it is subjected to different values of single‐ion anisotropy and magnetic fields. The increase in the strength of the magnetic field generates discontinuities in the magnetization, and the inversion of its polarity destroys the compensation points. Finally, a phase diagram is presented with the critical, spin compensation, and discontinuous temperatures in terms of the magnetic and anisotropic fields for the ferri‐ and ferromagnetic cases. The results are compared with a recent investigation of this system that does not include the antiferromagnetic next‐nearest‐neighbor interactions, which influences the magnetic behavior of the model.