Most existing examples of full conformal predictive systems, split conformal predictive systems, and cross-conformal predictive systems impose severe restrictions on the adaptation of predictive distributions to the test object at hand. In this paper we develop split conformal predictive systems that are fully adaptive. Our method consists in calibrating existing predictive systems; the input predictive system is not supposed to satisfy any properties of validity, whereas the output predictive system is guaranteed to be calibrated in probability.