Abstract Crescent-shaped plasmonic nanostructures can support surface plasmon resonance modes which, in most cases, basically reside around the tip and can be spectrally tunable by the geometry and size. In this work, we present a systematic numerical study of plasmon resonances in dimers of two opposing nanocrescents which have four tips in close proximity. It is shown that such dimer structures can support flexible tunable multipole resonances in the near-infrared. For transverse polarization, the dimer plasmon resonance peaks spectrally split around the first and the second order modes of the individual crescent, due to the strong plasmon coupling and hybridization which lead to bonding and anti-bonding symmetries. However, for longitudinal polarization, multipole plasmon modes are found in consequence and they are all blue-shifted spectrally for increased dimer gap. The blue-shift of the plasmon multipole resonances can be understood qualitatively within the framework of dipole–dipole interaction. These properties are observed in both two-dimensional and three-dimensional cases. They are therefore useful for crescent-based optical surface enhanced spectroscopy and for making plasmonic metamaterials.