The damping of two-dimensional plasmons in structures with several quantum wells due to absorption by free carriers is studied theoretically. Both gate structures and structures without a gate are considered. It is shown by the example of structures with GaAs quantum wells that an increase in the number of quantum wells while maintaining the electron concentration in each of them leads to a decrease in the damping coefficient of two-dimensional plasmons. The physical reasons for the decrease in the absorption of plasmons are discussed. It is shown that an increase in the number of quantum wells should lead to a decrease in the decay of plasmons in systems with a finite gate width as well.