arXiv:2607.06832v2 Announce Type: replace-cross Abstract: We investigate when multivariate kriging improves on separate prediction, using separable multi-output Gaussian processes as the principal theoretical benchmark. We introduce directed coverage, directed proximity and borrowing potential indices to describe design complementarity beyond exact overlap without response values. Under common radial kernels, we derive finite-design bounds linking geometry to prediction gains with known covariance parameters and information for estimating cross-output dependence. An exact risk decomposition under correct specification separates oracle gains from differences in estimation penalties; we give a mean-square expansion under explicit conditions. We distinguish parameter sharing from response coupling: auxiliary data can improve prediction through shared-scale estimation even when direct borrowing is negligible. This distinction guides a calibrated screening-and-validation procedure comparing separate marginal models, a shared-scale independent model and a coupled model, retaining the shared-scale option when coupling is excluded. In simulations with sparse target data and auxiliary observations retained during validation, the procedure reduces mean latent squared-error risk by 6.66% relative to separate fitting. After calibration, screening reduces runtime by 14.01% relative to direct validation of the same candidates, with similar mean risk. Controlled experiments show that covariance misspecification can reverse fitted gains, while queueing and monitoring applications demonstrate the importance of auxiliary coverage and the prediction task. These findings support task-matched validation and separate assessments of predictive accuracy, uncertainty calibration and computational cost.