We analyse high signal-to-noise ESPaDOnS/CFHT spectra of 20 very metal-poor (VMP) stars ([Fe/H] $\,\lt\,-2.0$) in the solar neighbourhood (within $\sim 2$ kpc), selected to be on planar orbits with maximum heights $\lesssim 4$ kpc. The sample comprises 11 stars on prograde and 9 on retrograde orbits, all with relatively high eccentricities (0.5─0.9). Their chemical abundance patterns indicate enrichment from high-energy supernovae and hypernovae up to the Fe-peak, and contributions from fast-rotating massive stars and neutron star mergers for the neutron-capture elements. No significant chemical differences are found between prograde and retrograde stars. The [Sr, Ba, Eu/Fe] ratios resemble those of stars in classical dwarfs galaxies. Chemical dispersion and distance analyses further highlight the internal similarity of the sample and its separation from the bulk of the observed, non-planar halo population. Applying the same kinematical selection to another homogeneous data set yields consistent results, confirming that this group of planar VMP stars exhibit peculiar chemical properties distinct from those of the observed halo and other known Galactic structures. These findings suggest that the stars formed in an environment that experienced a homogeneous chemical evolution akin to that of dwarf galaxies. A plausible scenario, supported by cosmological zoom-in simulations, is the early accretion of a single system whose subsequent dynamical evolution naturally produced stars on both prograde and retrograde planar orbits. If this interpretation is correct, we tentatively refer to this putative progenitor as Loki. However, comparisons with other planar VMP stars spanning a wider range of chemo-dynamical properties indicate that multiple accretion events likely contributed to this diverse population orbiting close to the Galactic plane.