A modular construction system, including, first and second walls, each having first and second broad surfaces. Each wall includes throughgoing connector-receiving bores. The modular construction system further includes a connector including a longitudinal body portion arranged along a longitudinal axis and having a first width. A head portion of the longitudinal body portion includes a base surface having a second width in a direction transverse to the longitudinal axis. A pair of protrusions extend outwardly from the longitudinal body portion and are disposed between the base surface and a tail end of the longitudinal body portion. The protrusions include an engagement surface facing toward the base surface and having a third width, the third width being greater than the first width.