We extend results first announced by Franz et al., that identified vA 351 = H346 in the Hyades as a multiple star system containing a white dwarf. With Hubble Space Telescope Fine Guidance Sensor fringe tracking and scanning, and more recent speckle observations, all spanning 20.7 years, we establish a parallax, relative orbit, and mass fraction for two components, with a period, $P=2.70\,\mathrm{yr}$ and total mass 2.1 ${{ \mathcal M }}_{\odot }$ . With ground-based radial velocities from the McDonald Observatory Otto Struve 2.1 m Telescope Sandiford Spectrograph, and Center for Astrophysics Digital Speedometers, spanning 37 years, we find that component B consists of BC, two M dwarf stars orbiting with a very short period ( ${P}_{\mathrm{BC}}=0.749$ days), having a mass ratio ${{ \mathcal M }}_{{\rm{C}}}$ / ${{ \mathcal M }}_{{\rm{B}}}$ = 0.95. We confirm that the total mass of the system can only be reconciled with the distance and component photometry by including a fainter, higher-mass component. The quadruple system consists of three M dwarfs (A, B, C) and one white dwarf (D). We determine individual M dwarf masses ${{ \mathcal M }}_{{\rm{A}}}$ = 0.53 ± 0.10 ${{ \mathcal M }}_{\odot }$ , ${{ \mathcal M }}_{{\rm{B}}}$ = 0.43 ± 0.04 ${{ \mathcal M }}_{\odot }$ , and ${{ \mathcal M }}_{{\rm{C}}}$ = 0.41 ± 0.04 ${{ \mathcal M }}_{\odot }$ . The white dwarf mass, 0.54 ± 0.04 ${{ \mathcal M }}_{\odot }$ , comes from cooling models, an assumed Hyades age of 670 Myr, and consistency with all previous and derived astrometric, photometric, and radial velocity results. Velocities from Hα and He I emission lines confirm the BC period derived from absorption lines, with similar (He I) and higher (Hα) velocity amplitudes. We ascribe the larger Hα amplitude to emission from a region each component shadows from the other, depending on the line of sight. * We dedicate this paper to John Stauffer, who died on 2021 January 29, in honor of his many contributions to the field.
