The experimental neutron and x-ray diffraction data for stoichiometric and S-deficient Ge(x)As(x)S(100-2x) glasses with x = 18.2, 25.0, and 33.3 at.% have been modeled simultaneously using the reverse Monte Carlo (RMC) technique. Nearest-neighbor coordination environments, as obtained in previous x-ray absorption spectroscopy and diffraction experiments, have been employed as short-range order constraints in these simulations. The large scale three-dimensional structural models thus obtained from RMC simulation are used to investigate the nature and compositional evolution of intermediate-range structural order in these ternary glasses. The intermediate-range structural order is controlled by (1) a corner-shared three-dimensional network of AsS(3) pyramids and GeS(4) tetrahedra in the stoichiometric Ge(18.2)As(18.2)S(63.6) glass, (2) a heterogeneous structure that consists of homopolar bonded As-rich regions coexisting with a GeS(2) network in the S-deficient Ge(25)As(25)S(50) glass, and (3) a homogeneous structure resulting from the disruption of the topological continuity of the GeS(2) network and As-rich clusters regions due to the formation of Ge-As bonds in the most S-deficient Ge(33.3)As(33.3)S(33.3) glass. This scenario of the compositional evolution of intermediate-range structural order is consistent with and provides an atomistic explanation of the corresponding evolution in the position, width and intensity of the first sharp diffraction peak and the magnitude of small angle scattering in these glasses.