In this work we not only presented an ecient implementation of the density fitted NEO-MP2 method for small to mid-size systems, we also for the first time introduced local approximations within a multicomponent correlation treatment. We demonstrated that with our approach large systems can be computed at a fraction of the computational costs of the canonical counterpart. As such, correlation energies including NQEs can be obtained in an efficient and accurate manner paving the way for their routine application in a suite of challenges, from ab initio drug development to material design. Our composite approach successfully describes systems where regular electronic structure methods are qualitatively and quantitatively incorrect. In future work we will continue improving our composite method in terms of accuracy by including the coupling of the electronic and nuclear amplitudes and finding more e cient ways to compute the electronicnuclear correlation. Moreover, we will also focus on implementing a local density fitted NEO-DFT method as well as a density fitted version of the NEO-TDDFT method. Both are needed within the NEO-DFT(V) method, which provides accurate vibrational frequencies with multicomponent methods. Besides the implementation work, tailoring nuclear auxil-iary fitting basis sets for the well established nuclear PB basis sets will further increase the accuracy and lower the computational costs of density fitted approaches.