Accurate face detection and subsequent localization of facial landmarks are mandatory in many computer vision applications, such as emotion recognition, age estimation, and gender identification. Thanks to advancements in deep learning, numerous applications were developed for human faces. However, many applications have to employ multiple models to accomplish various tasks. As a result, they require more memory usage and increased inference time. Also, less attention is paid to other domains, such as animals and cartoon characters. To address these challenges, we propose an input-agnostic face model, AnyFace++, to perform multiple face-related tasks concurrently. The tasks are face detection and prediction of facial landmarks for human, animal, and cartoon faces, as well as age estimation, gender classification, and emotion recognition for human faces. We trained the model using deep multi-task multi-domain learning with a heterogeneous cost function. The experimental results demonstrate that AnyFace++ generates outcomes comparable to those of cutting-edge models specifically designed for specific domains. We have made the source code and pre-trained model publicly available at https://github.com/IS2AI/AnyFacePP to bolster research in this area.