The thermal conductance of interfaces plays a major role in defining the thermal properties of nanostructured materials in which heat transfer is predominantly phonon mediated. Ongoing research has improved the understanding of factors that govern interfacial phonon transport as well as the ability to predict thermal interface conductance. However, despite this progress, the ability to control interface conductance remains a major challenge. In this manuscript, we present a method to enhance and tune thermal interface conductance at vibrationally mismatched solid-solid interfaces. Enhancement is achieved through the insertion of an interfacial film with mediating vibrational properties, such that the vibrational mismatch at the interface is bridged, and consequently, the total interface conductance is enhanced. This phenomena is explored using nonequilibrium molecular dynamics simulations, where the effects of altering the interfacial film thickness, vibrational spectrum, and the temperature of the system are investigated. A systematic study of these pertinent design parameters explores the ability to enhance and tune phonon transport at both ideal (sharp) and nonideal (compositionally disordered) interfaces. Results show that interface conductance can be broadly enhanced by up to 53% in comparison to the vibrationally mismatched baseline interface. Additionally, we find that compositional disorder at an interface does not imply a deterministic change in interface conductance, but instead, that the influence of compositional disorder depends on the characteristics of the disordered region itself. These results, in contrast to macroscopic thermal transport theory, imply that it is possible to increase thermal conductance associated with interface scattering by adding more material along the direction of heat flux.