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We explored the evolution of various properties of multiple-population globular clusters (GCs) for a broad range of initial conditions. We simulated over 200 GC models using theMOCCAMonte Carlo code and find that the present-day properties of core and half-light radii and the ratio of the number of second-generation (SG) stars to the total number of stars (N_SG/N_TOT) of these models cover the observed values of these quantities for Milky Way GCs. Starting with a relatively small value of the SG fraction (N_SG/N_TOT~ 0.25) and a SG system concentrated in the inner regions of the cluster, we find, in agreement with previous studies, that systems in which the first-generation (FG) is initially tidally filling or slightly tidally underfilling best reproduce the observed ratios of N_SG/N_TOTand have values of the core and half-light radii typical of those of many Galactic globular clusters. Models in which the FG is initially tidally underfilling retain values of N_SG/N_TOTclose to their initial values. These simulations expand previous investigations and serve to further constrain the viable range of initial parameters and better understand their influence on present-day GC properties. The results of this investigation also provide the basis for our future survey aimed at building specific models to reproduce the observed trends (or lack thereof) between the properties of multiple stellar populations and other cluster properties.