The Mindlin plate theory was initially developed to precisely analyze the vibration frequencies of crystal plates in the vicinity of the fundamental thickness-shear vibration mode. When investigating the overtone vibrations of quartz crystal plates, low-order theories often fail to provide sufficiently accurate solutions, necessitating the use of higher-order theories to enhance the precision of the analysis. To this objective, this study proposes a systematic symmetric correction scheme that extends the correction process of the Mindlin plate theory to the 11th-order. The correction factors maintain the symmetry of higher-order stress tensors, thereby ensuring compatibility in the finite element formulation. The corrected theory provides a more accurate description of the dispersion relationship, thereby significantly enhancing the accuracy in predicting vibration frequencies. The analytical results are verified by comparisons with the three-dimensional theory. Notably, these correction factors exhibit material anisotropy independence, substantially enhancing the universality and enabling broader applications across diverse material systems.