We use the spectroscopy and homogeneous photometry of 97 Type Ia supernovae (SNe Ia) obtained by the Carnegie Supernova Project as well as a subset of 36 SNe Ia presented by Zheng et al. to examine maximum-light correlations in a four-dimensional (4D) parameter space: B-band absolute magnitude, M-B, Si II lambda 6355 velocity, vSi II, and Si II pseudo-equivalent widths pEW(Si II lambda 6355) and pEW(Si II lambda 5972). 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 [MB, vSi II] space. Extending the GMM into the full 4D space yields a grouping system that only slightly alters group definitions in the [M-B, v(Si II)] projection, showing that most of the clustering information in [M-B, v(Si II)] is already contained in the 2D GMM groupings. However, the full 4D space does divide group membership for faster objects between corenormal and broad-line objects in the Branch diagram. A significant correlation between M-B and pseudo-equivalent width (Si II lambda 5972) 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 v(Si II), indicating that this subclass of SNe Ia may be somehow different from the other groups.