We present nonperturbative theoretical results showing a resonant-like enhancement of above-threshold detachment spectra in the region of the high-energy plateau as the laser intensity sweeps across channel thresholds. This enhancement has a pure quantum origin stemming from well-known threshold phenomena in multichannel problems whose features are clearly demonstrated in our numerical results. Similar well-known anomalies at neutral atom thresholds are expected to explain experimentally observed resonant-like enhancements of above-threshold ionization spectra.