Very recently, a new convective constraint release (CCR) single-mode (toy) model [Ianniruberto and Marrucci, J. Rheol. 58, 89-102 (2014)] has been proposed to account for the nowadays well-ascertained fact that flow induces some degree of disentanglement, the more so the faster is the flow [Baig et al., Macromolecules 43, 6886-6902 (2010)]. The previous work, successful in explaining some qualitative aspects of the nonlinear step strain response, is here extended to the multimode case by developing a model allowing for a spectrum of relaxation times in both orientational and stretch dynamics, the purpose being one of performing a quantitative comparison with literature data on nearly monodisperse linear polymers. Several data of relaxation after shear step strain and of time-dependent stress response in shear and elongational startup are considered. The overall agreement of the new multimode CCR model with data appears satisfactory. (C) 2015 The Society of Rheology.