Model-based damage identification for Structural Health Monitoring (SHM) remains an open issue in the literature. Along with the computational challenges related to the modeling of full-scale structures, classical single-model structural identification (St-Id) approaches provide no means to guarantee the physical meaningfulness of the inverse calibration results. In this light, this work introduces a novel concept of multi-class digital twins (DTs) formed by a population of competing models, each representing a different failure mechanism. The forward models in the DT are replaced by computationally efficient meta-models, and continuously calibrated using monitoring data. If an anomaly in the structural performance is detected, a model selection approach based on the Bayesian information criterion (BIC) is used to identify the most plausibly activated failure mechanism. The potential of the proposed approach is illustrated through two case studies, including a numerical planar truss and a real-world historical construction: the Muhammad Tower in the Alhambra fortress.