  We propose a general and experimentally feasible approach to realize
simultaneous ground-state cooling of arbitrary number of near-degenerate, or
even fully degenerate mechanical modes, overcoming the limit imposed by the
formation of mechanical dark modes. Multiple optical modes are employed to
provide different dissipation channels that prevent complete destructive
interference of the cooling pathway, and thus eliminating the dark modes. The
cooling rate and limit are explicitly specified, in which the
distinguishability of the optical modes to the mechanical modes is found to be
critical for an efficient cooling process. In a realistic multi-mode
optomechanical system, ground-state cooling of all mechanical modes is
demonstrated by sequentially introducing optical drives, proving the
feasibility and scalability of the proposed scheme. The work may provide new
insights in preparing and manipulating multiple quantum states in macroscopic
systems.
