The existence of a kinematically defined moving group of stars centred at U=-40, V=-17km/s, referred to as the Hyades supercluster, has been suggested to be the debris of an originally large star-forming event, with its core being the present-day Hyades open cluster. Using high-resolution UV-Visual Echelle Spectrograph (UVES) spectra, we present the elemental abundances for a range of alpha, Fe-peak and neutron-capture elements for 26 proposed supercluster stars. Our results show that the sample stars display a heterogeneous abundance distribution, with a clump around [Fe/H]=+0.15. We also calculate stellar radial velocities and U, V, W space velocities. Enforcing strict chemical and kinematical membership criteria, we find that four supercluster stars share the Hyades open cluster abundances and kinematics, while many of the remaining stars fit the disc field kinematics and abundance range. We discuss our findings in the context of the Hyades supercluster being a dispersed star-forming remnant, a stellar stream of purely dynamical origin or a result of several processes.