We test the hypothesis of $K(1460)$ being a hadronic $J^P=0^{-}$ molecule through nonperturbative $S$-wave $KK\overline{K}$, $K\pi \pi$, $K\pi \eta$ coupled-channel dynamics in a three-body unitary isobar approach. The scalar two-body coupled-channel resonances $f_0(500)$, $f_0(980)$, $a_0(980)$, and $K_0^{*}(700)$ are generated in the subsytems in amplitudes that match phase shifts from experiment. In a first step, previous results in the limit of mass-degenerate, stable $f_0$ and $a_0$ isobars are reproduced. Once the full seven-coupled channel model is switched on, other $S$-matrix effects obscure and modify the resonance signal, including complex thresholds, a two-body cusp, and a triangle singularity at threshold.

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• Hadron-hadron interactions
• Hadronic decays