The Raman scattering of bulk nonstoichiometric chalcogenide alloys along the pseudo-binary AsS₃ – GeS₄ tie-line, which completely lies in the intermediate phase (IP) region of As-S-Ge ternary system was investigated in order to reveal the structural transformations in charge of the unusual features of the middle range order, elastic and physical-chemical parameters of these glasses observed earlier. It is shown that very narrow compositional areas can form inside the IP with high level of structural self-organization, mainly due to sudden increase of the concentration of highly flexible species such as quasi-tetrahedral (QT) S=As(S_1/2)₃ s.u. that comprises 4-fold coordinated As atoms. In the (GeS₄)_x(AsS₃)_1-x ternary system such a compositional area appears around the Ge_7.7As_15.3S₇₇ (x =0.33; < r > = 2.31) composition that is a strongly self-organized glass with an assessed concentration of QT S=As(S_1/2)₃ around 30 % of total atomic clusters being the building blocks of the structure. This composition consists of minimal number of atomic building species, apart from QT S=As(S_1/2)₃ s.u. and free sulfur only the AsS₃ pyramids and edge-sharing (ES) GeS₄ tetrahedra have been revealed. Actually this self-organized state seems to be compositionally “metastable” as the variation of Ge concentrations by approximately ±3.5at% transforms the most part of the QT S=As(S_1/2)₃ s.u. into either AsS₃ pyramids or corner-sharing (CS) GeS₄ tetrahedra, mixed with a number of others clusters of smaller concentration. A good correlation was found between the compositional dependence of Raman scattering normalized strengths and middle range ordering (MRO) parameters such as sizes of molecular domains (D) and correlated inter-domain distances (d), as well as the molar volume (V_m) and longitudinal elastic modulus (C_L). MRO parameters and molar volume exhibit global minima around composition (As_15,3 S₇₇ Ge_7,7; x = 0.33; < r > = 2.31) corresponding to strong self - organized glass that assign it as glass with most “packed” MRO structure and meanwhile the elastic modulus reaches its maximum value.