Genetic minimal cut sets (gMCS) are sets of genes that must be deactivated simultaneously to avoid unwanted states in a metabolic model. The concept of gMCS can be applied to two different scenarios. First, it can be used to identify potential gene toxicities in generic or healthy cell models. Second, it can be used to develop genetic strategies to target cancer cells and prevent their proliferation. Up to now, gMCS have been evaluated using the traditional procedure of preventing biomass production. This paper proposes an additional way: using essential metabolic tasks, which any human cell should perform, to enlarge the set of unwanted states. Including this addition can greatly improve the study of toxicities and reveal targets that can be used to treat unhealthy cells. Excluding metabolic tasks can cause important information to be overlooked, which could impact the study’s success. Regarding toxicities, using the generic Human model, the number of detected generic toxicities with metabolic tasks increases from 106 to 281 (136 gMCSs of length 1 and 49 of length 2). For the evaluation of specific toxicities in different healthy tissues,we have used the following context-specific models: blood, pancreas, liver, heart, and kidney. Again, considering metabolic tasks, we have found new toxicities (both of lengths 1 and 2) whose inactivation could damage these healthy tissues. Our research strategy has been applied to identify new cancer drug targets in two myeloma cell lines. We obtained new therapeutic targets of lengths 1 and 2 for each cell line. After analyzing the data, we conclude that incorporating metabolic tasks into cancer models can reveal important therapeutic targets that were previously disregarded by the conventional method of inhibiting biomass production. This approach also improves the evaluation of potential drug toxicities.