The Ames mutagenicity test constitutes the most frequently used assay to estimate the mutagenic potential of drug candidates. While this test employs experimental results using various strains of Salmonella typhimurium, the vast majority of the published in silico models for predicting mutagenicity do not take into account the test results of the individual experiments conducted for each strain. Instead, such QSAR models are generally trained employing overall labels (i.e., mutagenic and nonmutagenic). Recently, neural-based models combined with multitask learning strategies have yielded interesting results in different domains, given their capabilities to model multitarget functions. In this scenario, we propose a novel neural-based QSAR model to predict mutagenicity that leverages experimental results from different strains involved in the Ames test by means of a multitask learning approach. To the best of our knowledge, the modeling strategy hereby proposed has not been applied to model Ames mutagenicity previously. The results yielded by our model surpass those obtained by single-task modeling strategies, such as models that predict the overall Ames label or ensemble models built from individual strains. For reproducibility and accessibility purposes, all source code and datasets used in our experiments are publicly available.