A games table features a unique corner assembly in which upper and lower corner members respectively embrace about upper and lower edges of an elongated perimeter frame member of the table and are clamped together to secure the frame member in place around a primary gameplay panel. Matable male and female features on the corner assemblies also enable stacking of two table top units to enable convenient switching of a games table between two modes of game play. Invertible caps of the corner units feature braces capable of receiving a second horizontal gameplay panel in a position over the primary gameplay panel. The main gameplay panel is double sided, whereby Inversion of the entire tabletop unit enables a second mode of gameplay. Alternatively, support arms of an upright gameplay unit featuring a basketball backboard or other upright panel are insertable into the corner units.