This design can be scaled across more sets of inserters/chests. Just change the constant on the combinator to the number of chests used and run the wires.
*Only works if one type of item exists across all connected chests

Originally shared on the public FactorioPrints / Factorio School archive (factorioprints.com · factorio.school). Authorship preserved from the public catalog.
This design can be scaled across more sets of inserters/chests. Just change the constant on the combinator to the number of chests used and run the wires.
*Only works if one type of item exists across all connected chests