The dynamics of magnetized plasma sheath with three isothermal ions is studied numerically using the fluid model. The three ions (Ar+, Kr+, and Xe+) are assumed to be singly charged and have the same temperature. In the beginning, the concentrations for Ar+ and Xe+ were taken in the same proportions, and then the Kr+ ion density is introduced slowly in the plasma. It is found that the presence of a third ion has changed the dynamics of ion densities inside the sheath and simultaneously their respective velocities. Ion density and electron density profiles were estimated inside the sheath region in the presence of a weak and strong magnetic field as well at different Kr+ion concentrations. Further, the dependence of magnetic field obliqueness on the ion density profile and its velocities inside the sheath is also studied, and observed ion density bunching at different conditions. Based on the results, we have tried to introduce a concept of the derivation of system Bohm velocity by considering the ion mass as equivalent mass for the three interacting ion systems in the plasma. It is found that the system Bohm velocity with the equivalent mass effect is larger than their individual thermal velocities and close to Ar+Bohm velocity, and higher than the system Bohm velocity with reference to the density ratio and their respective individual Bohm velocities in an isothermal multi-component plasma.