We use the spectroscopy and homogeneous photometry of 97 Type Ia supernovae obtained by the emph{Carnegie Supernova Project} as well as a subset of 36 Type Ia supernovae presented by Zheng et al. (2018) to examine maximum-light correlations in a four-dimensional (4-D) parameter space: $B$-band absolute magnitude, $M_B$, ion{Si}{2}~$lambda6355$ velocity, vsi, and ion{Si}{2} pseudo-equivalent widths pEW(ion{Si}{2}~$lambda6355$) and pEW(ion{Si}{2}~$lambda5972$). It is shown using Gaussian mixture models (GMMs) that the original four groups in the Branch diagram are well-defined and robust in this parameterization. We find three continuous groups that describe the behavior of our sample in [$M_B$, vsi] space. Extending the GMM into the full 4-D space yields a grouping system that only slightly alters group definitions in the [$M_B$, vsi] projection, showing that most of the clustering information in [$M_B$, vsi] is already contained in the 2-D GMM groupings. However, the full 4-D space does divide group membership for faster objects between core-normal and broad-line objects in the Branch diagram. A significant correlation between $M_B$ and pEW(ion{Si}{2}~$lambda5972$) is found, which implies that Branch group membership can be well-constrained by spectroscopic quantities alone. In general, we find that higher-dimensional GMMs reduce the uncertainty of group membership for objects between the originally defined Branch groups. We also find that the broad-line Branch group becomes nearly distinct with the inclusion of vsi, indicating that this subclass of SNe Ia may be somehow different from the other groups.
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