Higgs final states are prime targets in the search for physics beyond the Standard Model. In the conventional picture, symmetry together with the Goldstone Equivalence Theorem correlates Higgs and gauge-boson final states, implying comparable sensitivity in channels such as , , and in searches for heavy resonances. In this work, we identify a mechanism to parametrically violate this expectation. We show that higher-order Higgs couplings can induce an electroweak-symmetry-breaking enhancement that selectively amplifies Higgs-rich final states, allowing them to become the leading discovery channels of new resonances. For scalar resonances, this can make di-Higgs the dominant bosonic signal. For resonance masses higher than a couple of TeV, it also opens resonant tri-Higgs and four-Higgs channels as well-motivated search targets. The same underlying mechanism extends to heavy fermionic and vector resonances, where it can similarly enhance channels such as , , and . We present this framework in effective field theory, demonstrate possible UV completions, and discuss its implications for collider searches.

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