Structures that include a metal-insulator-metal (MIM) capacitor and methods for fabricating a structure that includes a MIM capacitor. The MIM capacitor includes a first electrode, a second electrode, and a third electrode. A conductive via is arranged in a via opening extending in a vertical direction through at least the first electrode. The first electrode has a surface arranged inside the via opening in a plane transverse to the vertical direction, and the conductive via contacts the first electrode over an area of the surface.