The collective excitation of the conduction electrons in subwavelength structures gives rise to the Localized Surface Plasmon(LSP). The system consisting of two such LSPs, known as the dimer system,is of fundamental interest and is being actively investigated in the literature. Three regimes have been previously identified and they are the photonic regime, the strong coupling regime and the quantum tunneling regime. In this Letter, we propose a new regime for this intriguing systems, the intermediate regime. In this new regime, the quasistatic approximation, which is widely used to study such LSP systems, fails to capture the main physics: the multiple scattering of the electromagnetic waves between the two LSPs, which significantly modifies the properties of the resonant modes in the system. This intermediate regime provides a new route to explore in plasmonics, where controlling both the excited plasmon modes and the damping rates are of paramount significance.