Road traffic crashes remain a major concern globally resulting in loss of life and worsening the quality of life and productivity of the crash survivors. The current study contributes to road safety literature by focusing on developing high resolution crash severity models based on driver injury severity reported using Abbreviated Injury Scale (AIS) by body region. For this purpose, the research develops a joint random parameters multivariate model structure with as many dimensions as severity by body location. The proposed model system is developed using Crash Injury Research Engineering Network (CIREN) data, which includes patients admitted to trauma centers due to a crash from 2005 to 2015. The dataset contained information about a comprehensive set of exogenous variables including driver characteristics, vehicle characteristics, crash characteristics, roadway characteristics, and environmental characteristics. The empirical analysis involves the estimation of Random Parameters Multivariate Generalized Ordered Probit Model that allows for the influence of common unobserved factors affecting the vehicle occupant severity across body locations. The model estimation results are further augmented by conducting elasticity analysis to highlight the differential impact of various factors on severity across body regions.