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The primary challenge in the study of explosive astrophysical transients is their detection and characterisation using multiple messengers. For this purpose, we have developed a new data-driven discovery framework, based on deep learning. We demonstrate its use for searches involving neutrinos, optical supernovae, and gamma rays. We show that we can match or substantially improve upon the performance of state-of-the-art techniques, while significantly minimising the dependence on modelling and on instrument characterisation. Particularly, our approach is intended for near- and real-time analyses, which are essential for effective follow-up of detections. Our algorithm is designed to combine a range of instruments and types of input data, representing different messengers, physical regimes, and temporal scales. The methodology is optimised for agnostic searches of unexpected phenomena, and has the potential to substantially enhance their discovery prospects.