Engineering of nanophotonic devices for controlling light requires deep understanding of the interaction between their subwavelength structure elements. Theoretical approaches based on the multiple scattering theory provide simple analytics valuable for design. However, they consider different elements separated by the surrounding medium. Here, we develop an approach to study wave coupling in the case of overlapping particles. We consider the simplest system-a dimer of nanopillars-and find that it can be described by a three-oscillator model. Two modes correspond to the multipole response of isolated particles that interact through radiating and evanescent waves in accordance with the conventional multiple scattering theory, but there exists a third effective non-resonant oscillator supporting a direct mode coupling via the intersecting part. Our simple model yields results with a reliable agreement with numerical simulations and allows insight into the physical processes underlying the collective response of a cluster of overlapped subwavelength particles.