We analyze resonant magnetoelastic interactions between standing perpendicular spin wave modes (exchange magnons) and longitudinal acoustic phonon modes in free-standing hybrid metal-ferromagnet bilayer and trilayer structures. Whereas the ferromagnetic layer acts as a magnetic cavity, all metal layers control the frequencies and eigenmodes of acoustic vibrations. The design proposed here allows for achieving and tuning the spectral and spatial mode overlap between phonons and magnons that results in their strong resonant interaction. Realistic simulations for gold-nickel multilayers show that sweeping the external magnetic field should allow for observing resonantly enhanced interactions between individual magnon and phonon modes in a broad range of frequencies spanning from tens of gigahertz up to several hundreds of gigahertz, which can be finely tuned through the multilayer design. Our results would enable the systematic study and the deep understanding of resonantly enhanced magnetoelastic coupling between individual phonon and magnon modes up to frequencies of great contemporary fundamental and applied interest.