A convertible furniture piece includes a base frame, pivotable arms connected to the base frame, and a back member rotatably connected to the pivotable arms, the back member comprising first and second portions coupled together by a linkage system. The connection of the pair of pivotable arms to the base frame comprises a first pivot point that enables translation of the back member between a generally upright couch position and a horizontal table position, with the first and second portions of the back member being joined in each of the couch position and the table position. The connection of the back member to the pair of pivotable arms comprises a second pivot point that enables translation of the back member between a generally upright couch position and a bed position, with the first and second portions of the back member being rotated relative to one another in the bed position.