The data-driven computational mechanics framework, initially developed for elastic material behavior, has been extended by various works to plasticity problems in recent years. The originally developed approach exploits an initial material dataset obtained from a single loading path, whereby dedicated model formalisms were established to determine a new admissible material dataset for the next plastic increment [1]. More recently, novel frameworks have been proposed that utilize datasets containing strain path changes and determine the admissible material states within such datasets [2]. Nevertheless, their application to the full solution on a three-dimensional continuum has so far been limited in the presence of kinematic hardening and when multiple load reversals are required due to the complexity of the required dataspace with higher dimensionality. A hybrid model/data-driven approach is here proposed where certain aspects of the simulation, ideally the ones that can be reliably resolved by a model or a constitutive assumption, are enriched by such models/assumptions, while the dataspace is used to resolve functional dependencies, which otherwise would require parameter identification. As such, linear elasticity, associative and J2 plasticity are assumed in this work. A specific functional dependency for kinematic hardening (governing the back stress evolution) is assumed as well whereby the precise functions remain undetermined. Similarly, a functional dependency for the isotropic hardening is assumed without stating the full form of the function. The dataspace is than used to resolve the functional dependencies in the incremental-iterative steps of a FEM simulation such as the implicit return-mapping. Additionally, a search direction approximating the elastoplastic tangent is defined via the dataspace. Viability of the required dataspace and its construction through simple tests is discussed. The performance of the proposed method is demonstrated both through one and three dimensional problems under complex loading conditions for Prager’s type kinematic hardening behavior.