A semiannular rectangular composite cavity structure based on metal-insulator-metal waveguides is proposed. By adding a rectangular cavity at a suitable position around the semiannular cavity (SAC), a single analogous plasmonic-induced absorption (PIA) effect is achieved at the expected mode of the SAC structure. After adding two rectangular cavities together in the SAC system, dual analogous PIA effects for both modes can be realized simultaneously. In addition, the phase response is also studied, and abnormal dispersions are achieved in the PIA windows, which can be used in the integrated optics for fast/slow light. The performances of the proposed two-dimensional structure are analyzed and studied by the coupled-mode theory and the finite-difference time-domain method, respectively.