We introduce a novel quantum-classical variational method that extends the quantum devices capabilities to approximate ground states of interacting quantum systems. The proposed method enhances parameterized quantum circuit ansatzes implemented on quantum devices with classical variational functions, such as neural-network quantum states. The quantum hardware is used as a high-accuracy solver on the most correlated degrees of freedom, while the remaining contributions are treated on a classical device. Our approach is completely variational, providing a well-defined route to systematically improve the accuracy by increasing the number of variational parameters, and performs a global optimization of the two partitions at the same time. We demonstrate the effectiveness of the protocol on spin chains and small molecules and provide insights into its accuracy and computational cost. We prove that our method is able to converge to exact diagonalization results via the addition of classical degrees of freedom, while the quantum circuit is kept fixed in both depth and width.