Using an expanded Brueckner–Hartree–Fock (BHF) framework with a phenomenological three-body force (3BF), we study the microscopic characteristics and equation of state (EOS) of symmetric nuclear and neutron matter. Both symmetric nuclear and pure neutron matter are used in the G-matrix computations, which are carried out by adding the 3BF to the initial two-body force (2BF) and employing a partial wave expansion. Using an angle-average and accurate Pauli operator, the single-particle potential is applied in both its standard and continuous forms. The fourth-order charge-dependent chiral nucleon–nucleon contact of the N3LO potential was used for the computations, both with and without the three-nucleon Urbana interaction included. It was found that the BHF approximation significantly improves the computations for symmetric nuclear matter at high density when one uses only the N3LO potential. As a matter of fact, it is shown that the 3BF is required for reproducing the empirical saturation property of symmetric nuclear matter in a non-relativistic microscopic framework and significantly alters the EOS of nuclear matter at huge densities above the typical nuclear matter density. A crucial component of the estimated equation of state of isospin-asymmetric nuclear matter is the nuclear symmetry energy. It establishes the structure of neutron stars and finite nuclei.