The Jahn-Teller (JT) coupling effects in the triply degenerate ground electronic state of methane radical cation are investigated theoretically within a quadratic vibronic coupling approach. The underlying potential energy surfaces over the two-dimensional space of nuclear coordinates, subject to the T(2) ⊗ (e + t(2) + t(2)) Jahn-Teller effect, are established from extensive ab initio calculations using the multi-reference configuration interaction method and then employed to determine the various parameters of a diabatic Hamiltonian of this system. Our previous investigation [T. Mondal and A. J. C. Varandas, J. Chem. Phys. 135, 174304 (2011)], relying on the linear vibronic coupling approach augmented by only a diagonal second-order term of the totally symmetric mode, are extended here by including all possible quadratic coupling constants of JT active e and t(2) modes. Inclusion of these quadratic couplings is found to be important to reproduce correctly the broad vibrational structure and for a better description of dynamical JT effect in the first vibronic band of this radical cation. The impact of large amplitude motions (which are responsible for floppiness of the molecule) on the vibronic structure and dynamics of the first photoelectron band have been examined via readjustment of their linear coupling parameters up to ±10%.