Fast and effective analytical screening tools providing new suitable authenticity markers and applicable to a large number of samples are required to efficiently control the global olive oil (OO) production, and allow the rapid detection of low levels of adulterants even with fatty acid composition similar to OO. The present study aims to develop authentication models for the comprehensive detection of illegal blends of OO with adulterants including different types of high linoleic (HL) and high oleic (HO) vegetable oils at low concentrations (2-10%) based on shotgun triacylglyceml (TAG) profile obtained by Flow Injection Analysis-Heated Electrospray Ionisation-High Resolution Mass Spectrometry (FIA-HESI-HRMS) at a large-scale experimental design. The sample set covers a large natural variability of both OO and adulterants, resulting in more than one thousand samples analysed. A combined PLS-DA binary modelling based on shotgun TAG profiling proved to be a fit for purpose screening tool in terms of efficiency and applicability. The external validation resulted in the correct classification of the 86.8% of the adulterated samples (diagnostic sensitivity = 0.87), and the 81.1% of the genuine samples (diagnostic specificity = 0.81), with an 85.1% overall correct classification (efficiency = 0.85).