Bound states in the continuum (BICs) enable elastic-wave resonances with ultralow radiation loss, but in multimode plates localized modes readily couple to multiple radiation channels. Here we extend a symmetry-mismatch design recently implemented in one-dimensional (1D) Lamb wave structures to a 2D phononic crystal plate and realize elastic BICs and quasi-BICs by exploiting a mismatch between symmetric (S) and antisymmetric (A) Lamb modes. The plate is engineered such that the A mode forms a passband while the S mode exhibits a bandgap; a central defect then hosts localized S modes whose eigenfrequencies lie in this bandgap yet overlap the A-mode continuum, forming S-mode BICs. Finite-element simulations and laser Doppler vibrometry show that the number of BIC modes can be controlled varying the number of defect unit cells. By weakly breaking the mid-plane mirror symmetry through tilted hole sidewalls, we induce controlled S–A hybridization and convert these strictly bound states into quasi-BICs that are efficiently excited by plane waves. Using this mechanism, we implement a planar multi-cavity structure where spatially separated quasi-BIC resonators are addressed at distinct frequencies, thereby realizing planar space–frequency multiplexing and providing a simple route to multifrequency elastic-wave signal processing and integrated phononic circuits.