  The simultaneous ground-state refrigeration of multiple vibrational modes is
a prerequisite for observing significant quantum effects of multiple-vibration
systems. Here we propose how to realize a large amplification in the
net-refrigeration rates based on cavity optomechanics and to largely improve
the cooling performance of multivibration modes beyond the resolved-sideband
regime. By employing an auxiliary mechanical coupling (AMC) between two
mechanical vibrations, the dark mode, which is induced by the coupling of these
vibrational modes to a common optical mode and cuts off cooling channels, can
be fully removed. We use fully analytical treatments for the effective
mechanical susceptibilities and net-cooling rates and find that when the AMC is
turned on, the amplification of the net-refrigeration rates by more than six
orders of magnitude can be observed. In particular, we reveal that the
simultaneous ground-state cooling beyond the resolved-sideband regime arises
from the introduced AMC, without which it vanishes. Our work paves the way for
quantum control of multiple vibrational modes in the bad-cavity regime.
