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High Entropy Alloys are a class of alloys which have been shown to largely exhibit stable microstructures, as well as frequently good mechanical properties, particularly when manufactured by additive manufacturing. Due to the large number of potential compositions that their multi-component nature introduces, high throughput alloy development methods are desirable to speed up the investigation of novel alloys. Here, we explore once such method, in-situ alloying during Additive Manufacture, where a powder of a certain pre-alloyed composition is mixed with the required composition of powder of an additional element, such that alloying takes place when powders are melted during the process. To test the effectiveness and capability of the approach, selective laser melting has been used to manufacture pre-alloyed CoCrFeNi, and also CoCrFeNiCu and CoCrFeNiTi alloys by combining pre-alloyed CoCrFeNi powder with elemental powders of Cu and Ti. Processing parameter variations are used to find the highest relative density for each alloy, and samples were then characterised for microstructure and phase composition. The CoCrFeNi alloy shows a single phase face centred cubic (FCC) microstructure, as found with other processing methods. The CoCrFeNiCu alloy has a two phase FCC microstructure with clear partitioning of the Cu, while the CoCrFeNiTi alloy has an FCC matrix phase with NiTi intermetallics and a hexagonal close packed (HCP) phase, as well as unmelted Ti particles. The microstructures therefore differ from those observed in the same alloys manufactured by other methods, mainly due to the presence of areas with higher concentrations than usually encountered of Cu and Ti respectively. Successful in-situ alloying in this process seems to be improved by the added elemental powder having a lower melting point than the base alloy, as well as a low inherent tendency to segregate. While not producing directly comparable microstructures however, the approach does seem to offer advantages for the rapid screening of alloys for AM processability, identifying, for example, extensive solid-state cracking in the CoCrFeNiTi alloy.