  We present an updated strong-lensing analysis of the massive cluster Abell
370 (A370), continuing the work first presented in Lagattuta et al. (2017). In
this new analysis, we take advantage of the deeper imaging data from the Hubble
Space Telescope (HST) Frontier Fields program, as well as a large spectroscopic
mosaic obtained with the Multi-Unit Spectroscopic Explorer (MUSE). Thanks to
the extended coverage of this mosaic, we probe the full 3D distribution of
galaxies in the field, giving us a unique picture of the extended structure of
the cluster and its surroundings. Our final catalog contains 584 redshifts,
representing the largest spectroscopic catalog of A370 to date. Constructing
the model, we measure a total mass distribution that is quantitatively similar
to our previous work -- though to ensure a low rms error in the model fit, we
invoke a significantly large external shear term. Using the redshift catalog,
we search for other bound groups of galaxies, which may give rise to a more
physical interpretation of this shear. We identify three structures in narrow
redshift ranges along the line of sight, highlighting possible infalling
substructures into the main cluster halo. We also discover additional
substructure candidates in low-resolution imaging at larger projected radii.
More spectroscopic coverage of these regions (pushing close to the A370 virial
radius) and more extended, high-resolution imaging will be required to
investigate this possibility, further advancing the analysis of these
interesting developments.
