We present a simplified stochastic model designed to exemplify the nonlinear rheology of entangled supramolecular polymeric materials. As a toy model for entanglement effects, we use the Rolie-Poly equations [Likhtman and Graham, J. Non-Newtonian Fluid Mech. 114, 1-12 (2003)] that we decorate with finite extensibility. Additionally, we include a stretch-dependent probability of detachment for the stickers. In both linear and nonlinear regimes, we explore the parameter space, indicating the parameter values for which qualitative changes in response to the applied flow are predicted. Theory and results in the linear rheology regime are consistent with the previous more detailed work of van Ruymbeke and co-workers [van Ruymbeke et al., Macromolecules 43, 4401-4411 (2010)]. Finally, we develop a preaveraged version of the stochastic equations described above to obtain a set of nonstochastic coupled equations that produces very similar predictions but requires less computing resources. This preaveraged model is based on two tensors representing the attached and detached chain populations and a scalar quantity that represents the fraction of these populations. (C) 2017 The Society of Rheology.