We present a dedicated search for gravitational-wave backgrounds with nontrivial peak structures using data from the first three and the initial part of the fourth observing runs of the LIGO-Virgo-KAGRA network. The analysis is motivated by a variety of early-Universe models characterized by signals with multiple peaks. We introduce a model independent parametrization of double-peaked spectra based on the superposition of two normalized broken power laws and perform a Bayesian inference study using the LIGO-Virgo-KAGRA isotropic cross-correlation data. While no statistically significant evidence for a multipeak background is found, the analysis provides constraints on the interpeak slopes in correlation with the signal amplitude. These results exhibit LIGO-Virgo-KAGRA’s ability to probe signals beyond a single peak structure and establish a foundation for future targeted searches for nontrivial gravitational waves background spectral shapes in future observing runs and the advanced detector era.

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• Gravitational waves