<p>The Modified Quasichemical Model has been further extended into the Distinguishable-Quadruplet Approximation (MQMDQA) to simultaneously account for first-nearest-neighbor short-range ordering (SRO), multiple compositions of second-nearest-neighbor SRO, and multiple compositions of reciprocal SRO in systems with two sublattices. When one sublattice is either fully occupied by a single species or remains empty, the model simplifies to the Modified Quasichemical Model for one sublattice in the Distinguishable-Pair Approximation. Moreover, when the coordination numbers and interaction energies of all distinguishable binary quadruplets (within each sub-binary system) and ternary reciprocal quadruplets (within each sub-ternary system) are uniformly defined—or when each system contains only a single binary and a single ternary reciprocal quadruplet—the MQMDQA fully reduces to the Modified Quasichemical Model in the Quadruplet Approximation (MQMQA). This compatibility between MQMDQA and MQMQA is especially significant, as it ensures that existing thermodynamic databases developed using MQMQA can be directly reused within MQMDQA without any modifications.</p>