Weak multivalent interactions between receptors and ligands can achieve super selectivity due to enhanced binding from multiple arms, enabling them to differentiate between surfaces with varying receptor densities. However, the theoretical understanding of multivalent binding including the effect of receptor depletion, binding kinetics, and the effect of incorporating different ligands within a single nanostar, is limited. This complicates the interpretations of experiments and restricts the therapeutic potential of multivalent particles. This study implements the Gillespie algorithm, to systemically study their binding kinetics, depletion effects, and the effect of incorporating two different ligands within a single nanostar. These simulations demonstrate a significant reduction in coverage, selectivity, and average number of arms bound per particle in equilibrium at the receptor density regime where receptor depletion is significant. Additionally, receptor depletion causes a dynamic competition between bound and unbound nanostars, leading to a decrease in the average number of arms bound over time. The populations of nanostars with i arms bound have a higher population selectivity than the selectivity considering all bound nanostars. Furthermore, incorporating two types of ligands can enhance selectivity. These insights advance our understanding of multivalent systems, offering the potential for incorporating multivalent particles in therapeutic applications.