The present work extends the multicoated micromechanical model of Lipinski (2006, “Micromechanical Modeling of an Arbitrary Ellipsoidal Multi-Coated Inclusion,” Philos. Mag., 86(10), pp. 1305–1326) in the quasistatic domain to compute the effective material moduli of a viscoelastic material containing multicoated spherical inclusions displaying elastic or viscoelastic behavior. Losses are taken into account by introducing the frequency-dependent complex stiffness tensors of the viscoelastic matrix and the multicoated inclusions. The advantage of the micromechanical model is that it is applicable to the case of nonspherical multicoated inclusions embedded in anisotropic materials. The numerical simulations indicate that with proper choice of material properties, it is possible to engineer multiphase polymer system to have a high-loss modulus (good energy dissipation characteristics) for a wide range of frequencies without substantially degrading the stiffness of the composite (storage modulus). The numerical analyses show also that with respect to the relative magnitudes of the loss factors and the storage moduli of the matrix, inclusion and coating, the overall properties of the viscoelastic particulate composite are dominated by the properties of the matrices in some frequency ranges. The model can thus be a suitable tool to explore a wide range of microstructures for the design of materials with high capacity to absorb acoustic and vibrational energies.