We simulate the linear and nonlinear rheology of two different viscoelastic polymer solutions, a polyisobutylene solution in pristane and an aqueous solution of hydroxypropylcellulose, using a highly coarse-grained approach known as Responsive Particle Dynamics (RaPiD) model. In RaPiD, each polymer has originally been depicted as a spherical particle with the effects of the eliminated degrees of freedom accounted for by an appropriate free energy and transient pairwise forces. Motivated by the inability of this spherical particle representation to entirely capture the nonlinear rheology of both fluids, we extended the RaPiD model by introducing a deformable particle capable of elongation. A Finite-Extensible Non-Linear Elastic potential provides a free energy penalty for particle elongation. Upon disentangling, this deformability allows more time for particles to re-entangle with neighbouring particles. We show this process to be integral towards recovering the experimental nonlinear rheology, obtaining excellent agreement. We show that the nonlinear rheology is crucially dependent upon the maximum elongation and less so on the elasticity of the particles. In addition, the description of the linear rheology has been retained in the process.