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, MB, Si ii λ6355 velocity, , and Si ii pseudo-equivalent widths pEW(Si ii λ6355) and pEW(Si ii λ5972). 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, space. Extending the GMM into the full 4D space yields a grouping system that only slightly alters group definitions in the MB, projection, showing that most of the clustering information in MB, is already contained in the 2D GMM groupings. However, the full 4D space does divide group membership for faster objects between core-normal and broad-line objects in the Branch diagram. A significant correlation between MB and pseudo-equivalent width (Si ii λ5972) 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 , indicating that this subclass of SNe Ia may be somehow different from the other groups.