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Faced with changing markets and evolving consumer demands, beef industries are investing in grading systems to maximise value extraction throughout their entire supply chain. The Meat Standards Australia (MSA) system is a customer-oriented total quality management system that stands out internationally by predicting quality grades of specific muscles processed by a designated cooking method. The model currently underpinning the MSA system requires laborious effort to estimate and its prediction performance may be less accurate in the presence of unbalanced data sets where many "muscle x cook" combinations have few observations and/or few predictors of palatability are available. This paper proposes a novel predictive method for beef eating quality that bridges a spectrum of muscle x cook-specific models. At one extreme, each muscle x cook combination is modelled independently; at the other extreme a pooled predictive model is obtained across all muscle x cook combinations. Via a data-driven regularization method, we cover all muscle x cook-specific models along this spectrum. We demonstrate that the proposed predictive method attains considerable accuracy improvements relative to independent or pooled approaches on unique MSA data sets.