Deploying deep learning models in time-critical applications with limited computational resources, for instance in edge computing systems and IoT networks, is a challenging task that often relies on dynamic inference methods such as early exiting. In this paper, we introduce a novel architecture for early exiting based on the vision transformer architecture, as well as a fine-tuning strategy that significantly increase the accuracy of early exit branches compared to conventional approaches while introducing less overhead. Through extensive experiments on image and audio classification as well as audiovisual crowd counting, we show that our method works for both classification and regression problems, and in both single-and multi-modal settings. Additionally, we introduce a novel method for integrating audio and visual modalities within early exits in audiovisual data analysis, that can lead to a more fine-grained dynamic inference.