In recent years, surrogate models that combine conventional machine learning techniques with physical constraints have gained popularity in the material modeling community due to their improved generalization capabilities compared to purely data-driven models. However, these models are usually specialized to a narrow range of material models and have limited applicability in an important computationally demanding application: concurrent multiscale simulations. In the multiscale approach, complex materials with history dependence are taken into account without a constitutive model at the macroscale through the use of a representative volume element (RVE), or a micromodel. At the microscale, regular constitutive models are then assigned to the constituents. In [1], we proposed a hybrid model, the Physically Recurrent Neural Network (PRNN), to predict the macroscopic stress of heterogeneous and path-dependent materials. The core idea is to combine an encoder-decoder architecture with embedded constitutive models. The encoder learns a set of values, interpreted as strains, that are fed to the same constitutive models as in the RVE. These in turn compute the stress and, in the case of a history-dependent model, the updated internal variables of the (fictitious) material point. The collection of fictitious stresses is passed to the decoder to obtain the macroscopic stresses, while the internal variables are automatically updated according to the physics postulated in the constitutive model, effectively working as the memory of the network. This combination results in great generalization properties with small training sets and offers a clear interpretation of its latent space. In this work, we investigate how the knowledge of the latent space can be leveraged to perform two tasks concurrently: predicting the macroscopic stress and the maximum hydrostatic microscopic stress, a potential indicator of macroscopic material failure. With the same architecture as in [1] to perform the first task, we now calculate the hydrostatic stress of all fictitious material points. From this pool, the maximum value is selected to compute the loss of the second task, which is added to the loss of the first task. For a heterogeneous RVE with elastoplastic medium and elastic inclusions, we show that the multi-task approach requires no additional training data compared to the one-task PRNN. Furthermore, we explore the interpretability of the latent space by comparing the [...]