In this work, we investigate the asymptotic behavior of the eigenvalues of the classical Steklov problem in a thin multidomain as the thickness parameter tends to zero. The multidomain consists of two vertically aligned cylinders, one placed above the other. We show that the eigenvalues converge to zero as the domain becomes thinner. In this setting, the limiting eigenvalue problem in the upper cylinder reduces to a one-dimensional problem, whereas the limiting problem in the lower cylinder is posed on an $(n-1)$-dimensional ball. Finally, we consider the case in which the upper and lower cylinders have the same order of thickness.