The additive manufacturing of metals by material extrusion in a multi-step process (MEX-MSt/M) represents a special process variant of the commonly used material extrusion (MEX) and is based on the processing of highly filled polymer filaments. This technology uses the geometrical freedom and fast processing given by MEX to create individual metal parts after a debinding and sintering process in a cost and time-efficient way. The filaments for MEX-MSt/M are made by incorporating metal powders, such as aluminum, stainless steel, or bronze into a polymer matrix. Due to the challenges that are assigned to the processing of highly filled polymers, like the increased viscosity of the material or clogging of the nozzle, the binder materials have to meet several requirements. Therefore, waxes are often used to enable a better extrusion behavior for MEX; however, the addition of wax also affects other crucial processing properties of the filaments. In this work, the interactions of different types and amounts of waxes on thermal, mechanical, and rheological properties were investigated to create a better understanding of the alternating effects of wax addition into highly filled filaments for processing via MEX. The study demonstrated that an increase in wax contents resulted in both a significant decrease in ductility and an overall improvement in melt flowability. The choice of waxes also affected the particle–matrix interactions, partly leading to an improved wetting of the filler particles.