WaRSwap is a randomization algorithm that for the first time provides a practical network motif discovery method for large multi-layer networks, for example those that include transcription factors, microRNAs, and non-regulatory protein coding genes. The algorithm is applicable to systems with tens of thousands of genes, while accounting for critical aspects of biological networks, including self-loops, large hubs, and target rearrangements. We validate WaRSwap on a newly inferred regulatory network from Arabidopsis thaliana, and compare outcomes on published Drosophila and human networks. Specifically, sustained input switches are among the few over-represented circuits across this diverse set of eukaryotes.