The development of new substrates for surface-enhanced spectroscopy is primarily motivated by the ability to design such substrates to provide the maximum signal enhancement. In this paper, we theoretically design and investigate a crisscross dimer array as a plasmonic substrate for enhancing coherent anti-Stokes Raman scattering (CARS). The plasmonic film-crisscross dimer array system can excite multiple resonances at optical frequencies. By properly designing structure parameters, three plasmon resonances with large field enhancements and same spatial hot spot regions can spectrally match with the pump, Stokes and anti-Stokes beams, respectively. The CARS signals are strongly enhanced by multi-resonance plasmon field enhancements. The estimated CARS factor can reach as high order as ~1016 over conventional CARS without the plasmonic substrate.