<jats:p><jats:italic>Aims.</jats:italic> We present a spectroscopic analysis of the extremely luminous red star VX Sgr based on high-resolution observations combined with AAVSO light curve data. Given the puzzling characteristics of VX Sgr, we explore three scenarios for its nature: a massive red supergiant (RSG) or red hypergiant (RHG), a Thorne Żytkow object, and an extreme asymptotic giant branch (AGB) star.</jats:p> <jats:p><jats:italic>Methods.</jats:italic> Sampling more than one whole cycle of photometric variability, we derive stellar atmospheric parameters by using state-of-the-art PHOENIX atmospheric models. We compare them to optical and near-infrared spectral types. We report on some key features due to neutral elemental atomic species such as Li <jats:sc>I</jats:sc>, Ca <jats:sc>I</jats:sc>, and Rb <jats:sc>I</jats:sc>.</jats:p> <jats:p><jats:italic>Results.</jats:italic> We provide new insights into its luminosity, its evolutionary stage, and its pulsation period. Based on all the data, there are two strong reasons to believe that VX Sgr is some sort of extreme AGB star. Firstly, it has Mira-like behaviour during active phases. VX Sgr shows light variation with amplitude that is much larger than any known RSG and clearly larger than all RHGs. In addition, it displays Balmer line emission and, as shown here for the first time, line doubling of its metallic spectrum at maximum light, both characteristics typical of Miras. Secondly, unlike any known RSG or RHG, VX Sgr displays strong Rb <jats:sc>I</jats:sc> lines. In addition to the photospheric lines that are sometimes seen, it always shows circumstellar components whose expansion velocity is compatible with that of the OH masers in the envelope, demonstrating a continuous enrichment of the outer atmosphere with <jats:italic>s</jats:italic>-process elements, a behaviour that can only be explained by a third dredge-up during the thermal pulse phase.</jats:p>