The model recently proposed by the authors [J.Rheol.,45 (2001) 1305-1318] to account for convective constraint release (CCR) and chain stretch in entangled polymers is here extended to a multiple mode situation. Such an extension, indispensable for the polydisperse case, is believed to be important also for monodisperse polymers, especially in view of chain-end fluctuations. The model is compared with existing steady and transient start-up data of shear flows. It is also shown how the model can help explaining the frequently observed power-laws, especially for the case of melts.