© 2021 Elsevier B.V.The thermal variations of the order-parameters are investigated to study the phase diagrams of the ±J Blume–Capel (BC) model in the lowest approximation of the cluster variation method (LACVM). The bilinear exchange interaction parameter J is either turned on ferromagnetically with probability p or antiferromagnetically with 1−p on the sublattices to simulate the ±J BC model. The inclusion of external magnetic field reveals many extra features which is absent otherwise. The model presents up to two first-order and three second-order phase transitions. In addition to the ferromagnetic (FM), antiferromagnetic (AFM), ferrimagnetic (FI) and paramagnetic (PM) phases, chaotic regions are also observed which maybe signaling the existence of spin glass phase. The model displays tetracritical points in addition to the double reentrant behavior.