The paper considers the problem of estimating a covariate parameter shared by multiple statistical models. Under the objective of estimating the parameter with target reliability with the fewest number of samples from these models, a fundamental question is how to glean samples from the statistical models. This question is especially important when the models are not equally descriptive or informative about the parameter, each being the most informative only for a specific regime of the parameter. This paper provides 1) an active sampling framework that specifies how the samples should be collected from different models over time in a data-adaptive fashion; 2) a stopping criterion specifying when the collected data is informative enough to form a reliable estimate for the covariate parameter; and 3) a terminal estimation rule. These rules, collectively, are shown to admit certain optimality guarantees. Numerical evaluations are provided to compare the performance with relevant existing approaches.