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The complex solidification cycles experienced by multi-principal element alloys (MPEAs) during laser-based additive manufacturing (LBAM) often lead to structural defects that affect the build quality. The underlying thermal processes and phase transformations are a function of the process parameters employed. With a moving Gaussian heat source to mimic LBAM and leveraging material thermodynamics guidelines from CALculation of PHAse Diagrams (CALPHAD), we estimate the temperature-dependent thermal properties, phase fractions, and melt pool geometry using an experimentally validated computational fluid dynamics model. The results substantiate that the peak temperatures are inversely correlated to the scan speeds, and the melt pool dimensions can assist in the predictive selection of process parameters such as hatch distance and layer thickness. A relatively low cooling rate recorded during the process is ascribed to the preheating of the substrate to ensure printability of the alloy.