One weight for many variables: why multipurpose calibration of non-probability samples needs flexible working models, and what sharing it costs

National statistical offices apply one weight column to every variable, while the doubly robust and machine-learning adjustments that non-probability sources require are outcome-specific; reconciling the two is open. We construct one multipurpose production weight: a response-propensity pseudo-weight followed by a model calibration that stacks K study variables, each with its own learner, and is exactly consistent with the known population totals. The output is a single column an office publishes once and applies to every indicator and domain, disseminated with replicate weights whose variance propagates the whole estimated pipeline. With linear working models exact consistency faces a rank ceiling; escaping it needs predictions that do not share one linear span, through adaptive learners or cross-fitting. Because the calibration targets are estimated on a reference survey, whether its sampling error enters the standard error is a choice, and a consequential one: holding those targets fixed divides the estimated standard error by up to 3.7 and takes the coverage of a nominal 95 % interval to 42 % . Simulations on real household-survey microdata price the sharing: the binding limit is set by the failure mode rather than by K alone, and the cost concentrates on the rarest indicator.