Lectins, phytic acid and condensed tannins exert major antinutritional effects in common bean when grains are consumed as a staple food. In addition, phaseolin, i.e., the major storage protein of the bean seed, is marginally digested when introduced in the raw form. Our breeding target was to adjust the nutrient/antinutrient balance of the bean seed for obtaining a plant food with improved nutritional value for human consumption. In this study, the seeds of twelve phytohaemagglutinin-E-free bean lines carrying the mutations low phytic acid, phytohaemagglutinin-L-free, α-Amylase inhibitors-free, phaseolin-free, and reduced amount of condensed tannins, introgressed and differently combined in seven genetic groups, were analyzed for their nutrient composition. Inedited characteristics, such as a strong positive correlation (+0.839**) between the genetic combination “Absence of phaseolin + Presence of the α-Amylase Inhibitors” and the amount of “accumulated iron and zinc”, were detected. Three lines carrying this genetic combination showed a much higher iron content than the baseline (+22.4%) and one of them in particular, achieved high level (+29.1%; 91.37 µg g−1) without any specific breeding intervention. If confirmed by scientific verification, the association of these genetic traits might be usefully exploited for raising iron and zinc seed content in a bean biofortification breeding program.