A paper sheet handling apparatus comprising: a base module; and a first extension module connected to the base module in a horizontal direction, wherein the base module includes a feeding unit configured to receive paper sheets inside of the base module; a first transport unit configured to transport the paper sheets fed by the feeding unit; a recognition unit configured to recognize the paper sheets transported by the first transport unit; a plurality of first stacking units configured to stack the paper sheets based on the recognition result of the recognition unit, the plurality of first stacking units being arranged along the horizontal direction and each having an opening on a front face side of the paper sheet handling apparatus such that the stacked paper sheets are removable through the opening; and a control unit that is configured to control transport of the paper sheet based on the recognition unit, and is configured to control various structural components with which the base module and the first extension module are provided, and the first extension module includes a second transport unit configured to receive, inside of the first extension module, the paper sheets discharged from the base module by the first transport unit, and transport the paper sheets inside of the first extension module; and a plurality of second stacking units configured to stack the paper sheets transported by the second transport unit based on the recognition result of the recognition unit, the plurality of second stacking units being arranged along a vertical direction and each having an opening on the front face side of the paper sheet handling apparatus such that the stacked paper sheets are removable through the opening, wherein the control unit is configured to control the transport of the paper sheets recognized by the recognition unit to at least one of the plurality of first stacking units and the plurality of second stacking units. a base module; and a first extension module connected to the base module in a horizontal direction, wherein the base module includes a feeding unit configured to receive paper sheets inside of the base module; a first transport unit configured to transport the paper sheets fed by the feeding unit; a recognition unit configured to recognize the paper sheets transported by the first transport unit; a plurality of first stacking units configured to stack the paper sheets based on the recognition result of the recognition unit, the plurality of first stacking units being arranged along the horizontal direction and each having an opening on a front face side of the paper sheet handling apparatus such that the stacked paper sheets are removable through the opening; and a control unit that is configured to control transport of the paper sheet based on the recognition unit, and is configured to control various structural components with which the base module and the first extension module are provided, and a feeding unit configured to receive paper sheets inside of the base module; a first transport unit configured to transport the paper sheets fed by the feeding unit; a recognition unit configured to recognize the paper sheets transported by the first transport unit; a plurality of first stacking units configured to stack the paper sheets based on the recognition result of the recognition unit, the plurality of first stacking units being arranged along the horizontal direction and each having an opening on a front face side of the paper sheet handling apparatus such that the stacked paper sheets are removable through the opening; and a control unit that is configured to control transport of the paper sheet based on the recognition unit, and is configured to control various structural components with which the base module and the first extension module are provided, and the first extension module includes a second transport unit configured to receive, inside of the first extension module, the paper sheets discharged from the base module by the first transport unit, and transport the paper sheets inside of the first extension module; and a plurality of second stacking units configured to stack the paper sheets transported by the second transport unit based on the recognition result of the recognition unit, the plurality of second stacking units being arranged along a vertical direction and each having an opening on the front face side of the paper sheet handling apparatus such that the stacked paper sheets are removable through the opening, a second transport unit configured to receive, inside of the first extension module, the paper sheets discharged from the base module by the first transport unit, and transport the paper sheets inside of the first extension module; and a plurality of second stacking units configured to stack the paper sheets transported by the second transport unit based on the recognition result of the recognition unit, the plurality of second stacking units being arranged along a vertical direction and each having an opening on the front face side of the paper sheet handling apparatus such that the stacked paper sheets are removable through the opening, wherein the control unit is configured to control the transport of the paper sheets recognized by the recognition unit to at least one of the plurality of first stacking units and the plurality of second stacking units.