  We propose a variational scheme to represent composite quantum systems using
multiple parameterized functions of varying accuracies on both classical and
quantum hardware. The approach follows the variational principle over the
entire system, and is naturally suited for scenarios where an accurate
description is only needed in a smaller subspace. We show how to include
quantum devices as high-accuracy solvers on these correlated degrees of
freedom, while handling the remaining contributions with a classical device. We
demonstrate the effectiveness of the protocol on spin chains and small
molecules and provide insights into its accuracy and computational cost.
