Most successes in computational protein engineering to date have focused on enhancing one biophysical trait, while multi-trait optimization remains a challenge. Different biophysical properties are often conflicting, as mutations that improve one tend to worsen the others. In this study, we explored the potential of an automated computational design strategy, called CamSol Combination, to optimize solubility and stability of enzymes without affecting their activity. Specifically, we focus on Bacillus licheniformis α-amylase (BLA), a hyper-stable enzyme that finds diverse application in industry and biotechnology. We validate the computational predictions by producing 10 BLA variants, including the wild-type (WT) and three designed models harbouring between 6 and 8 mutations each. Our results show that all three models have substantially improved relative solubility over the WT, unaffected catalytic rate and retained hyper-stability, supporting the algorithm's capacity to optimize enzymes. High stability and solubility embody enzymes with superior resilience to chemical and physical stresses, enhance manufacturability and allow for high-concentration formulations characterized by extended shelf lives. This ability to readily optimize solubility and stability of enzymes will enable the rapid and reliable generation of highly robust and versatile reagents, poised to contribute to advancements in diverse scientific and industrial domains.