A sheet stacking system includes a conveyor for carrying sheets from a conveyor intake end to a conveyor discharge end and a hopper at the discharge end for receiving the sheets and guiding them as they fall in a cascade path onto a platform. The hopper has a backstop facing the discharge end of the conveyor and a first accumulator that includes a carrier and a support extending from the carrier through the backstop. The support is configured to rotate from a retracted position to an extended position relative to the backstop, and the carrier is movable linearly and vertically relative to the backstop with the support in the extended position from a raised location with the support outside the cascade path to a lowered location with the support in the cascade path.