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There is a growing push to evolve away from early warning systems that focus exclusively on what a hazard might be (e.g., in terms of magnitude or intensity), towards approaches that facilitate more meaningful decision-making based on the societal impacts a hazard might cause. These advanced, impact-based early warning systems should integrate alert or action thresholds that are calibrated using risk metrics derived from relevant engineering vulnerability models and (uncertain) forecasts of potential event amplitudes. Several impact-based (i.e., risk-informed) decision-making approaches for early warning have been proposed in the literature to address this requirement, particularly in the context of earthquakes and floods. They have been designed for application to a range of infrastructure, including railways, ports, roads, and buildings.However, current risk-informed early warning approaches implicitly assume that the associated decision to trigger (or not) action is being made in a single-hazard context, where the incoming event is the first hazard to which the infrastructure of interest has been exposed. This means that their alert thresholds are calibrated based on engineering vulnerability models (or other related information) for intact infrastructure assets, which could lead to suboptimal decision-making in multi-hazard-prone regions where infrastructure may have already experienced prior damage. We address this important limitation by introducing a risk-informed early warning decision-making framework for explicit application in multi-hazard contexts. The framework builds on previous earthquake early warning-related studies to provide a means of impact-based decision making on early warning alert issuance (action triggering) in the face of (possibly uncertain) existing infrastructure damage conditions due to previous events. The framework can handle a flexible amount of information related to the prior state of an engineering asset, from a definitive description of damage to probabilistic data on the intensity of the previous event it was exposed to. We demonstrate the framework for a hypothetical case-study building in the context of an earthquake sequence, considering a range of information about its initial conditions. We find that the best action for a given incoming event can depend on the building’s initial state, reinforcing the importance of accounting for damage accumulation when making decisions to issue early warnings.