Accurate face detection and subsequent localization of facial landmarks are mandatory steps in many computer vision applications, such as emotion recognition, age estimation, and gender identification. Thanks to advancements in deep learning, numerous facial applications have been developed for human faces. However, most have to employ multiple models to accomplish several tasks simultaneously. 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, including 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 cutting-edge models designed for specific domains.