We analyse shear stress and normal stress data obtained by cone-partitioned-plate (CPP) shear rheometry in recent years. The data sets of Schweizer et al. (Rheol. Acta 47, 943-957, 2008) and Costanzo et al. (Macromolecules 49, 3925-3935, 2016; & Fluids 4, 28, 2019) on nearly monodisperse polystyrene melts and solutions are considered to be among the most reliable shear data available. The Doi-Edwards independent alignment (DEIA) model (J. Chem. Soc., Faraday Transactions 2: Molecular and Chemical Physics 74, 1802-1832, 1978a,b) allows for quantitative description of the steady-state values of shear viscosity eta((gamma)over dot) and first normal stress coefficient psi(1)((gamma)over dot), while it underpredicts the stress overshoot of the stress growth coefficient of the shear stress, eta(+)(t), and fails in predicting a stress overshoot of the stress growth coefficient of first normal stress difference, psi(+)(1)(t). On the other hand, the extended interchain pressure (EIP) model (J. Rheol. 64, 95-110, 2020) provides an excellent prediction of the stress overshoots of both shear stress and first normal stress difference, while overpredicting the steady-state shear viscosity and the first normal stress coefficient. We demonstrate that the shear stress overshoot is the result of a combination of orientational stress overshoot and stretch overshoot, while the normal stress overshoot depends solely on the overshoot of the stretch. Based on these considerations, we propose a novel constitutive approach consisting of a combination of the DEIA and the EIP model, and predictions of this approach are found to be in quantitative agreement with the data sets of Schweizer et al. and Costanzo et al. within experimental accuracy.