Cosolvents modulate the stability of protein conformations and exhibit contrasting effects on the kinetics of aggregation by globular proteins and intrinsically disordered proteins (IDPs). The growth of ordered protein aggregates after the initial nucleation step is believed to proceed through a dock-lock mechanism. We have studied the effect of two denaturants [guanidinium chloride (GdmCl) and urea] and four protective osmolytes (trimethylamine N-oxide (TMAO), sucrose, sarcosine, and sorbitol) on the free energy surface (FES) of the dock-lock growth step of protein aggregation using a coarse-grained protein model and metadynamics simulations. We have used the proteins cSrc-SH3 and A beta(9-40) as model systems representing globular proteins and IDPs, respectively. The effect of cosolvents on protein conformations is taken into account using the molecular transfer model (MTM). The computed FES shows that protective osmolytes stabilize the compact aggregates, while denaturants destabilize them for both cSrc-SH3 and A beta(9-40). However, protective osmolytes increase the effective energy barrier for the multistep domain-swapped dimerization of cSrc-SH3, which is critical to the growth of protein aggregates by globular proteins, thus slowing down the overall aggregation rate. Contrastingly, denaturants decrease the effective barrier height for cSrc-SH3 dimerization and hence enhance the aggregation rate in globular proteins. The simulations further show that cSrc-SH3 monomers unfold before dimerization and the barrier to monomer unfolding regulates the effective rate of aggregation. In the case of IDP, A beta(9-40), protective osmolytes decrease and denaturants increase the effective barriers in the dock-lock mechanism of fibril growth, leading to faster and slower growth kinetics, respectively.