  A mechanism for generating primordial black-hole mass spectra with many
spikes is proposed and investigated. This mechanism relies on the choice of
non-Bunch-Davies vacua, these leading to oscillatory features in the
inflationary power spectrum. This in turn generates oscillations in the
primordial black-hole mass function with exponentially enhanced spikes. This
``multimodal'' effect is demonstrated for most of the well-studied models of
primordial black-hole formation.
