This paper continues our recent studies of the flow behavior of a two-fluid Rolie-Poly approximation for entangled polymer solutions. The model studied is similar to that used in our previous work, but now incorporates isotropic elastic contributions to the stress, as required for thermodynamic consistency. These contributions play no role in the dynamics of a single phase, incompressible polymer fluid. However, in the two-fluid model, each fluid phase, the polymer and the solvent, is compressible, and the isotropic elastic contribution to the stress cannot be neglected. We show that this change in the model leads to the prediction of a high Weissenberg number linear instability in simple shear flow, in addition to the linear instability at lower Weissenberg numbers that was identified in our preceding study. We then consider the dynamics of the full nonlinear system for both linear shear flow and the Taylor Couette geometry. The linear shear flow solutions are used primarily to explore the details of the flow that develops from the high Weissenberg number instability. The Taylor Couette geometry is studied for gap widths that are wide enough to allow detailed experimental measurements, and one primary focus is then to follow the transient evolution of the flow. We show that the time to reach steady state becomes very long as the gap width increases. However, the velocity and concentration distributions both show significant changes and banded structures for much smaller times, thus suggesting that the Taylor Couette geometry is a practical system for experimental studies and can be directly compared with the present theory. (C) 2016 The Society of Rheology.