In this work, we introduce the first multitasking model for quantitative structure-biological effect relationships focused on the simultaneous exploration of antibacterial activity against Gram-negative pathogens and in vitro safety profiles related to absorption, distribution, metabolism, elimination, and toxicity (ADMET). The multitasking model for quantitative structure-biological effect relationships was created from a data set containing 46,229 cases, and it exhibited accuracy higher than 97% in both training and prediction (test) sets. Several molecular fragments present in the compounds of the data set were selected, and their contributions to multiple biological effects were calculated, providing useful insights toward the detection of 2D pharmacophores, toxicophores, etc. Here, we used a fragment-based philosophy known as puzzle approach, where different fragments with positive contributions against all the biological effects (antibacterial activity and ADMET properties) were assembled as pieces of a puzzle, leading to the creation of six new molecules. Such assembly was dictated by the physicochemical interpretations of the different molecular descriptors of the model. The new molecules were predicted to exhibit potent activity against Gram-negative bacteria, and desirable ADMET properties. The druglikeness of these new molecules was in agreement with the Lipinski’s rule of five, making them promising candidates for future biological testing in the framework of collaborative drug discovery.