The importance of both recycling and additive manufacturing (AM) is increasing; however, there has been a limited focus on the development of AM alloys that are compatible in terms of recyclability with the larger scrap loops of wrought 5xxx, 6xxx and cast 3xx aluminium alloys. In this work, the powder bed fusion (PBF) printability of AlMgSi alloys in the interval of 0-30 wt% Mg and 0-4 wt% Si is screened experimentally with a high-throughput method. This method produces PBF-mimicked material by PVD co-sputtering, followed by laser remelting. Strong evidence was found for AlMgSi alloys being printable within two different composition ranges: Si + Mg < 0.7 wt% or for Si + 2/3 Mg > 4 wt% when Mg < 3 wt% and Si > 3 wt%. Increasing the amount of Mg and Si influences the grain structure by introducing fine columnar grains at the melt pool boundary, although the melt pool interior was unaffected. Hardness in an as-built state increased with both Mg and Si, although Si had a neglectable effect at low levels of Mg. Both the evaporative loss of Mg and the amount of Mg in solid solution increased linearly with the amount of Mg.