We present simulations of the mechanism of secondary nucleation of polymer crystallization, based on a new model accounting for the microscopic kinetics of attaching and detaching. As the key feature of the model, we introduced multibody-interaction parameters that establish correlations between the attaching and detaching rate constants and the resulting thickness and width of the crystalline lamella. Using MATLAB and Monte Carlo method, we followed the evolution of the secondary nuclei as a function of various multibody-interaction parameters. We identified three different growth progressions of the crystal: i) widening, ii) thickening and iii) simultaneously thickening and widening of lamellar crystals, controlled by the corresponding kinetic parameters.