Over the last decades, the search for fast and efficient transportation systems has raised the interest toward maglev technologies. In this scenario, the Hyperloop paradigm is regarded as a breakthrough for future mobility. However, its practical implementation requires the solution of key shortcomings. Among these, the stability of the electrodynamic levitation system remains partially unexplored. The state of the art presents numerous attempts to attain stable behavior. In recent works, the stabilization of maglev vehicles has been addressed only for the vertical dynamics. Nevertheless, stable operation of all degree-of-freedom is required for a successful implementation of these transportation systems. The present paper addresses the full stabilization of a downscaled vehicle where levitation and guidance are provided by electrodynamic means. To this end, a design methodology supported by analytical modeling is proposed, where the degree-of-freedom are stabilized by suitably introducing secondary suspension elements. The design of the secondary suspension and the guidance system is obtained through the optimization of stability and dynamic performance. Then, a multibody model is developed. Both numerical approaches are compared in the frequency domain for validation purposes. Finally, the multibody model is simulated in the time domain to assess system performance in the presence of track irregularities and evaluate coupling effects between the degree-of-freedom.