In this paper, a new strategy is proposed based on arbitrary selection of perturbation in a dielectric metasurface to achieve multiple quasi-bound states in the continuum (BICs) with identical modes under dual polarizations. Three distinct symmetry-broken perturbations are discussed. By selecting an arbitrary perturbation, triple quasi-BICs can be induced in transverse magnetic polarization modes at wavelengths of 1071.18, 1098.8, and 1199.6 nm, respectively. Simultaneously, double quasi-BICs at wavelengths of 1375.9 and 1628.5 nm are generated in transverse electric polarization modes. Moreover, the excited quasi-BICs exhibit excellent sensing performance with a maximum sensitivity of 900 nm/RIU, which is better than similar previous studies.