In spite of the popularity of end-to-end diarization systems nowadays, modular systems comprised of voice activity detection (VAD), speaker embedding extraction plus clustering, and overlapped speech detection (OSD) plus handling still attain competitive performance in many conditions. However, one of the main drawbacks of modular systems is the need to run (and train) different modules independently. In this work, we propose an approach to jointly train a model to produce speaker embeddings, VAD and OSD simultaneously and reach competitive performance at a fraction of the inference time of a standard approach. Furthermore, the joint inference leads to a simplified overall pipeline which brings us one step closer to a unified clustering-based method that can be trained end-to-end towards a diarization-specific objective.