Epigenetics has become a focus of interest in drug discovery. In this sense, bromodomain-containing proteins have emerged as potential epigenetic targets in cancer research and other therapeutic areas. Several computational approaches have been applied to the prediction of bromodomain inhibitors. Nevertheless, such approaches have several drawbacks such as the fact that they predict activity against only one bromodomain-containing protein, using structurally related compounds. Also, there are no reports focused on meaningfully analyzing the physicochemical/structural features that are necessary for the design of a bromodomain inhibitor. This work describes the development of two different multi-target models based on quantitative structure–activity relationships (mt-QSAR) for the prediction and in silico design of multi-target bromodomain inhibitors against the proteins BRD2, BRD3, and BRD4. The first model relied on linear discriminant analysis (LDA) while the second focused on artificial neural networks. Both models exhibited accuracies higher than 85% in the dataset. Several molecular fragments were extracted, and their contributions to the inhibitory activity against the three BET proteins were calculated by the LDA model. Six molecules were designed by assembling the fragments with positive contributions, and they were predicted as multi-target BET bromodomain inhibitors by the two mt-QSAR models. Molecular docking calculations converged with the predictions performed by the mt-QSAR models, suggesting that the designed molecules can exhibit potent activity against the three BET proteins. These molecules complied with the Lipinski’s rule of five.