A dispenser for storing and dispensing multiple rolls of sheet material is described. The rolls are held in place within the interior space of the housing by a pair of spindle holders. The housing front cover has an opening and a slidable door disposed therein to provide access to the rolls. A restricting member is movably coupled to the housing interior and biased to move in a direct towards an outmost winding of a roll. As the roll is dispensed, the restricting member moves out of the pathway of the door, eventually allowing a user to slide the door across the opening so that a second roll may be accessed.