Two shingled streams of signatures are stacked independently of each other in separate stacking bins (29,31) that are aligned vertically one above the other and also vertically aligned with the collection bin (32) of a re-feeder. The collection bin is replenished periodically by stopping the shingled streams and unloading the contents of the lower and upper stacking bins to form a combined stack of signatures in the re-feeder collection bin. Signatures in the re-feeder collection bin are delivered by an out-feed conveyor belt (68) in a single reshingled stream of signatures to an in-line processing station. In an alternative embodiment, the stacking bins are laterally separated with respect to each other for separately stacking signatures from two incoming shingled streams that are being output from separate web presses or other independent sources.