The design of advanced alloys specifically tailored to additive manufacturing processes is a research field that is attracting ever-increasing attention. Laser powder-bed fusion (LPBF) commonly uses pre-alloyed, fine powders (diameter usually 15–45 µm) to produce fully dense metallic parts. The availability of such fine, pre-alloyed powders reduces the iteration speed of alloy development for LPBF and renders it quite costly. Here, we overcome these drawbacks by performing in-situ alloying in LPBF starting with pure elemental powder mixtures avoiding the use of costly pre-alloyed powders. Pure iron, chromium, and nickel powder mixtures were used to perform in-situ alloying to manufacture 304 L stainless steel cube-shaped samples. Process parameters including scanning speed, laser power, beam diameter, and layer thickness were varied aiming at obtaining a chemically homogeneous alloy. The scientific questions focused on in this work are: which process parameters are required for producing such samples (in part already known in the state of the art), and why are these parameters conducive to homogeneity? Analytical modelling of the melt pool geometry and temperature field suggests that the residence time in the liquid state is the most important parameter controlling the chemical homogeneity of the parts. Results show that in-situ alloying can be successfully employed to enable faster and cost-efficient rapid alloy development.