The tunable multiple plasmon-induced transparency (PIT) effect is investigated numerically in a metal-insulator-metal (MIM) waveguide with three side-coupled rectangular resonators. The system exhibits dual-mode PIT effects in the visible and near-infrared regions. By adjusting the geometrical parameters of the structure, we can manipulate not only each single PIT window, but also the double PIT windows simultaneously. Our structures may have potential applications for optical communication, integrated optics, and optical information processing. The finite element method (FEM) illustrates our theoretical design.