Disclosed are a multi-sheet buffer module and a modular printing system incorporating the buffer module. The buffer module includes a primary sheet transport path that extends horizontally across a frame. Vertical buffer paths extend downward and upward from the primary sheet transport path. Each buffer path connects to a secondary sheet transport path, which provides a loop back connection to the primary sheet transport path. As a stream of sheets moves along the primary sheet transport path, sheets printed out of order will be selectively diverted into the sheet buffer paths. Then, at the proper moment, the sheet buffer paths will feed the buffered sheets into the secondary sheet transport path(s), which will transport them to the primary sheet transport path, such that they are inserted at the proper locations back into the stream of sheets.