Stars with unusual elemental abundances offer clues about rare astrophysical events or nucleosynthetic pathways. Stars with significantly depleted magnesium and enhanced potassium ([Mg/Fe] < -0.5; [K/Fe] > 1) have to date only been found in the massive globular cluster NGC 2419 and, to a lesser extent, NGC 2808. The origin of this abundance signature remains unknown, as does the reason for its apparent exclusivity to these two globular clusters. Here we present 112 field stars, identified from 454,180 LAMOST giants, that show significantly enhanced [K/Fe] and possibly depleted [Mg/Fe] abundance ratios. Our sample spans a wide range of metallicities (-1.5 < [Fe/H] < 0.3), yet none show abundance ratios of [K/Fe] or [Mg/Fe] that are as extreme as those observed in NGC 2419. If confirmed, the identified sample of stars represents evidence that the nucleosynthetic process producing the anomalous abundances ratios of [K/Fe] and [Mg/Fe] probably occurs at a wide range of metallicities. This would suggest that pollution scenarios that are limited to early epochs (such as Population III supernovae) are an unlikely explanation, although they cannot be ruled out entirely. This sample is expected to help guide modelling attempts to explain the origin of the Mg-K abundance signature.