Simultaneous ground-state cooling of multiple degenerate mechanical modes is a difficult issue in optomechanical systems, owing to the existence of the dark mode effect. Here we propose a universal and scalable method to break the dark mode effect of two degenerate mechanical modes by introducing cross-Kerr (CK) nonlinearity. At most, four stable steady states can be achieved in our scheme in the presence of the CK effect, unlike the bistable behavior of the standard optomechanical system. Under a constant input laser power, the effective detuning and mechanical resonant frequency can be modulated by the CK nonlinearity, resulting in an optimal CK coupling strength for cooling. Similarly, there will be an optimal input laser power for cooling when the CK coupling strength stays fixed. Our scheme can be extended to break the dark mode effect of multiple degenerate mechanical modes by introducing more than one CK effect. To fulfill the requirement of the simultaneous ground-state cooling of N multiple degenerate mechanical modes, N − 1 CK effects with different strengths are needed. Our proposal provides new, to the best of our knowledge. insights into dark mode control and might pave the way to manipulating multiple quantum states in a macroscopic system.