Co-excitations of diverse non-radiative scattering states in a single metasurface are promising for multifunctional nanophotonic devices. Anapole and bound state in the continuum (BIC) are two typical manifestations of nonradiation; however, it is challenging to simultaneously support them in a single metasurface. We propose and experimentally demonstrate all-dielectric Si-based dimer metasurfaces supporting magnetic anapole and quasi-BICs in the optical communication band. By exploiting inherent meta-atom resonator interactions and transforming dimer structures, we achieve dual-band high-Q resonances (one magnetic anapole and one quasi-BIC) and tri-band high-Q resonances (one magnetic anapole and two quasi-BICs) within a single metasurface. For the tri-band resonances, the measured Q-factors are 321.0 at 1508.5 nm, 313.4 at 1535.5 nm, and 287.1 at 1693.7 nm, respectively. Additionally, the magnetic anapole state always persists throughout the entire structural transformation processes, and the effect of structural parameter variation on its formation is investigated. Our work provides insights into the design of multifunctional metasurfaces supporting multiple non-radiative scattering states; it also could advance magnetic anapole applications associated with magnetic molecules or magneto-optic effects.