Recent developments in metallic additive manufacturing (AM) processes for the production of high-performance industrial pieces have been hampered by the limited availability of reliably processable or printable alloys. To date, most of the alloys used in AM are commercial grades that have been previously optimized for different manufacturing techniques. This study aims to design new alloys specifically tailored for AM processes, to minimize defects in the final products and to optimize their properties. A computational approach is proposed to design novel and optimized austenitic alloy compositions. This method integrates a suite of predictive tools, including machine learning, calculation of phase diagrams (CALPHAD) and physical models, all piloted by a multiobjective genetic algorithm. Within this framework, several material-dependent criteria are examined and their impact on properties and on the occurrence of defects is identified. To validate our approach, experimental tests are performed on a selected alloy composition: powder is produced by gas atomization and samples are fabricated by laser powder bed fusion. The microstructure and mechanical properties of the alloys are evaluated and its printability is compared with a commercial 316L stainless steel taken as a reference. The optimized alloy performs similarly to 316L in terms of coefficient of thermal expansion, hardness and elongation, but has a 17% lower yield strength and ultimate tensile strength (UTS), indicating that further optimization is required.