Melt-quenched AsxGexSe1–2x glasses over the composition range, 0 < x < 0.26, are examined in Raman scattering, T-modulated Differential Scanning Calorimetry (MDSC), and 119Sn Mossbauer spectroscopy measurements. The non-reversing enthalpy near Tg, ΔHnr(x), accessed from MDSC shows a global minimum (∼ 0) in the xc(1) = 0.09 < x < xc(2) = 0.16 range, and increases by an order of magnitude both at x < xc(1) and at x > xc(2). Raman mode frequency of corner-sharing Ge(Se1/2)4 tetrahedra studied as a function of x, also shows three distinct regimes (or power-laws, p) that coincide with ΔHnr(x) trends. These regimes are identified with mechanically floppy (x < xc(1)), intermediate (xc(1) < x < xc(2)), and stressed-rigid (x > xc(2)) phases. The Raman elasticity power-law in the intermediate phase, p1 = 1.04(3), and in the stressed rigid phase, p2= 1.52(5), suggest effective dimensionalities of d = 2 and 3 respectively.