Most existing time-to-event methods focus on either single-event or competing-risks settings, leaving multi-event scenarios relatively underexplored. In many healthcare applications, for example, a patient may experience multiple clinical events, that can be non-exclusive and semi-competing. A common workaround is to train independent single-event models for such multi-event problems, but this approach fails to exploit dependencies and shared structures across events. To overcome these limitations, we propose MENSA (Multi-Event Network for Survival Analysis), a deep learning model that jointly learns flexible time-to-event distributions for multiple events, whether competing or co-occurring. In addition, we introduce a novel trajectory-based likelihood term that captures the temporal ordering between events. Across four multi-event datasets, MENSA improves predictive performance over many state-of-the-art baselines. Source code is available at https://github.com/thecml/mensa.