Abstract We consider a novel deep three-dimensional (3D) optical superlattice (OSL) for the trapping and long-term 3D confinement of resonant impurity atoms immersed in a cold buffer gas. This OSL provides reliable isolation of the atoms from the vessel walls containing the gas mixture. Its operating principle is based on utilizing nonlinear interference phenomena within the light-induced drift effect and effective rectified forces arising from the interaction of an atom with a non-monochromatic light field. This concept was previously proposed and analyzed (for the case of a bichromatic field) in our prior work Krasnov (2024 Laser Phys. Lett. 21 095501) using a simple scalar (two-level) atom-field interaction model, which permitted the description of only two-dimensional atomic localization within an OSL. The present work generalizes these results to the case of four-level atoms with an F = 0 → F = 1 transition and a 3D configuration of multi-frequency optical fields.