We propose a design strategy for hybrid metamaterials with alternating phononic plates and pentamode units that produce complete bandgaps for elastic waves. The wave control relies on the simultaneous activation of two scattering mechanisms in the constituent elements. The approach is illustrated by numerical results for a configuration comprising phononic plates with cross-like cavities. We report complete bandgaps of tunable width due to variations of geometric parameters. We show that the wave attenuation performance of the hybrid metamaterials can be further enhanced through implementation of lightweight multiphase material compositions. These give rise to efficient wave attenuation in challenging low-frequency regions. The proposed design strategy is not limited to the analyzed cases alone and can be applied to various designs of phononic plates with cavities, inclusions or slender elements. Published by AIP Publishing.