Context. The solar vicinity is currently populated by a mix of stars with various chemo-dynamic properties, including stars with a high metallicity compared to the Sun. Dynamical processes such as churning and blurring are expected to relocate such metal-rich stars from the inner Galaxy to the solar region. Aims. We report the identification of a set of old super-metal-rich (+0.15 ≤ [Fe/H] ≤ +0.50) dwarf stars with low eccentricity orbits (e ≲ 0.2) that reach a maximum height from the Galactic plane in the range ∼0.5–1.5 kpc. We discuss their chemo-dynamic properties with the goal of understanding their potential origins. Methods. We used data from the internal Data Release 6 of the Gaia-ESO Survey. We selected stars observed at high resolution with abundances of 21 species of 18 individual elements (i.e. 21 dimensions). We applied a hierarchical clustering algorithm to group the stars with similar chemical abundances within the complete chemical abundance space. Orbits were integrated using astrometric data from Gaia and radial velocities from Gaia-ESO. Stellar ages were estimated using isochrones and a Bayesian method. Results. This set of super-metal-rich stars can be arranged into five subgroups, according to their chemical properties. Four of these groups seem to follow a chemical enrichment flow, where nearly all abundances increase in lockstep with Fe. The fifth subgroup shows different chemical characteristics. All the subgroups have the following features: median ages of the order of 7–9 Gyr (with five outlier stars of estimated younger age), solar or subsolar [Mg/Fe] ratios, maximum height from the Galactic plane in the range 0.5–1.5 kpc, low eccentricities (e ≲ 0.2), and a detachment from the expected metallicity gradient with guiding radius (which varies between ∼6 and 9 kpc for the majority of the stars). Conclusions. The high metallicity of our stars is incompatible with a formation in the solar neighbourhood. Their dynamic properties agree with theoretical expectations that these stars travelled from the inner Galaxy due to blurring and, more importantly, to churning. We therefore suggest that most of the stars in this population originated in the inner regions of the Milky Way (inner disc and/or the bulge) and later migrated to the solar neighbourhood. The region where the stars originated had a complex chemical enrichment history, with contributions from supernovae types Ia and II, and possibly asymptotic giant branch stars as well.