In collider-based particle and nuclear physics experiments, data are produced at such extreme rates that only a subset can be recorded for later analysis. Typically, algorithms select individual collision events for preservation and store the complete experimental response. A relatively new alternative strategy is to additionally save a partial record for a subset of events, allowing for later specific analysis of a larger fraction of events. We propose a strategy that bridges these paradigms by compressing entire events for generic offline analysis but at a lower fidelity. An optimal-transport-based β Variational Autoencoder (VAE) is used to automate the compression and the hyperparameter β controls the compression fidelity. We introduce a new approach for multi-objective learning functions by simultaneously learning a VAE appropriate for all values of β through parameterization. We present an example use case, a di-muon resonance search at the Large Hadron Collider (LHC), where we show that simulated data compressed by our β VAE has enough fidelity to distinguish distinct signal morphologies.